Method and apparatus for transmitting PBCH and method and apparatus for receiving PBCH

ABSTRACT

In a wireless communication system, a physical broadcast channel (PBCH) is encoded based on a Polar code and then is transmitted. Half-frame information within the PBCH is mapped to a bit position 247 among bit positions of the Polar code and synchronization signal and PBCH block (SSB) index information within the PBCH is mapped to bit positions 253, 254, and 255 of the Polar code.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation application of U.S. application Ser.No. 16/247,842, filed on Jan. 15, 2019, now allowed, which is acontinuation application of PCT International Application No.PCT/KR2018/013919, filed on Nov. 14, 2018, which claims the benefit ofU.S. Provisional Application Nos. 62/587,451, filed on Nov. 16, 2017;62/591,763, filed on Nov. 28, 2017; 62/592,354, filed on Nov. 29, 2017;and 62/593,221, filed on Nov. 30, 2017, which are all herebyincorporated by reference herein in their entirety.

TECHNICAL FIELD

The present invention relates to a wireless communication system, andmore particularly, to a method and apparatus for transmitting/receivinga physical broadcast channel (PBCH).

BACKGROUND

With appearance and spread of machine-to-machine (M2M) communication,machine type communication (MTC) and a variety of devices such assmartphones and tablet Personal Computers (PCs) and technology demandinga large amount of data transmission, data throughput needed in acellular network has rapidly increased. To satisfy such rapidlyincreasing data throughput, carrier aggregation technology, cognitiveradio technology, etc. for efficiently employing more frequency bandsand multiple input multiple output (MIMO) technology, multi-base station(BS) cooperation technology, etc. for raising data capacity transmittedon limited frequency resources have been developed.

As more communication devices have demanded higher communicationcapacity, there has been necessity of enhanced mobile broadband (eMBB)relative to legacy radio access technology (RAT). In addition, massivemachine type communication (mMTC) for providing various services anytimeand anywhere by connecting a plurality of devices and objects to eachother is one main issue to be considered in future-generationcommunication.

Further, a communication system to be designed in consideration ofservices/UEs sensitive to reliability and latency is under discussion.The introduction of future-generation RAT has been discussed by takinginto consideration eMBB communication, mMTC, ultra-reliable andlow-latency communication (URLLC), and the like.

SUMMARY

Due to introduction of new radio communication technology, the number ofuser equipments (UEs) to which a BS should provide a service in aprescribed resource region increases and the amount of data and controlinformation that the BS should transmit to the UEs increases. Since theamount of resources available to the BS for communication with the UE(s)is limited, a new method in which the BS efficiently receives/transmitsuplink/downlink data and/or uplink/downlink control information usingthe limited radio resources is needed. In other words, as the density ofnodes and/or the density of UEs increases, a method of efficiently usinghigh-density nodes or high-density UEs for communication is needed.

With development of technologies, overcoming delay or latency has becomean important challenge. Applications whose performance criticallydepends on delay/latency are increasing. Accordingly, a method to reducedelay/latency compared to the legacy system is demanded.

In a new communication system, use of Polar codes is considered toimprove channel coding performance. The size of Polar codes is generallymuch greater than that of other codes used for channel coding.Therefore, when Polar codes are used for channel coding, a method ofimproving a decoding speed of Polar codes is needed.

The technical objects that can be achieved through the present inventionare not limited to what has been particularly described hereinabove andother technical objects not described herein will be more clearlyunderstood by persons skilled in the art from the following detaileddescription.

In an aspect of the present invention, provided herein is a method oftransmitting a physical broadcast channel (PBCH) by a transmittingdevice in a wireless communication system. The method comprises: mappinginformation within the PBCH to bit positions of a Polar code of sizeN=512, based on a Polar sequence; encoding the information based on thePolar code; and transmitting the PBCH including the information. Theinformation includes half-frame information and synchronization signaland PBCH block (SSB) index information. The half-frame information is 1bit and is mapped to a bit position 247 among bit positions 0 to 511 ofthe Polar code. The SSB index information is 3 bits and is mapped to bitpositions 253, 254, and 255 of the Polar code.

In another aspect of the present invention, provided herein is a methodof receiving a physical broadcast channel (PBCH) by a receiving devicein a wireless communication system. The method comprises: receiving thePBCH; and decoding information within the PBCH based on a Polar code ofsize N=512. The information is decoded based on a mapping relationshipbetween the information and bit positions of the Polar code. Theinformation includes half-frame information and synchronization signaland PBCH block (SSB) index information. The half-frame information isone bit and the SSB index information is 3 bits. The mappingrelationship includes: mapping the half-frame information to a bitposition 247 among bit positions 0 to 511 of the Polar code, and mappingthe SSB index information to bit positions 253, 254, and 255 of thePolar code.

In a further aspect of the present invention, provided herein is atransmitting device for transmitting a physical broadcast channel (PBCH)in a wireless communication system. The transmitting device comprises atransceiver, and a processor operably connected to the transceiver. Theprocessor is configured to: map information within the PBCH to bitpositions of a Polar code of size N=512, based on a Polar sequence;encode the information based on the Polar code; and control thetransceiver to transmit the PBCH including the information. Theinformation includes half-frame information and synchronization signaland PBCH block (SSB) index information. The half-frame information isone bit and the processor is configured to map the half-frameinformation to a bit position 247 among bit positions 0 to 511 of thePolar code. The SSB index information is 3 bits and the processor isconfigured to map the SSB index information to bit positions 253, 254,and 255 of the Polar code.

In a still further aspect of the present invention, provided herein isreceiving device for receiving a physical broadcast channel (PBCH) in awireless communication system. The transmitting device comprises: atransceiver, and a processor operably connected to the transceiver. Theprocessor is configured to: control the transceiver to receive the PBCH;and decode information within the PBCH based on a Polar code of sizeN=512. The information is decoded based on a mapping relationshipbetween the information and bit positions of the Polar code. Theinformation includes half-frame information and synchronization signaland PBCH block (SSB) index information. The half-frame information isone bit and the SSB index information is 3 bits. The mappingrelationship includes: mapping the half-frame information to a bitposition 247 among bit positions 0 to 511 of the Polar code, and mappingthe SSB index information to bit positions 253, 254, and 255 of thePolar code.

In each aspect of the present invention, a total payload size of thePBCH including the information may be 56 bits.

In each aspect of the present invention, the Polar sequence may includea sequence arranging bit indexes 0 to 511 corresponding one by one tothe bit positions 0 to 511 of the Polar code in ascending order ofreliability.

In each aspect of the present invention, the information may include asystem frame number for a frame to which the PBCH belongs. In eachaspect of the present invention, the second and third least significantbits of the system frame number may be mapped to bit positions 441 and469 of the Polar code, respectively. In each aspect of the presentinvention, the other 8 bits of the system frame number may be mapped tobit positions 367, 375, 415, 444, 470, 473, 483 and 485 of the Polarcode.

The above technical solutions are merely some parts of the examples ofthe present invention and various examples into which the technicalfeatures of the present invention are incorporated can be derived andunderstood by persons skilled in the art from the following detaileddescription of the present invention.

According to example(s) of the present invention, uplink/downlinksignals can be efficiently transmitted/received. Therefore, overallthroughput of a radio communication system can be improved.

According to example(s) of the present invention, delay/latencyoccurring during communication between a user equipment and a basestation may be reduced.

According to example(s) of the present invention, decoding speed can beimproved when Polar codes are used for channel coding.

According to example(s) of the present invention, a block error rate(BLER) can be improved by allocating a specific bit to a specific bitposition of Polar codes.

It will be appreciated by persons skilled in the art that that theeffects that can be achieved through the present invention are notlimited to what has been particularly described hereinabove and otheradvantages of the present invention will be more clearly understood fromthe following detailed description.

BRIEF DESCRIPTION OF THE DRAWINGS

The accompanying drawings, which are included to provide a furtherunderstanding of the invention, illustrate examples of the invention andtogether with the description serve to explain the principle of theinvention.

FIG. 1 illustrates a transport block processing procedure in anLTE/LTE-A system.

FIG. 2 is a block diagram illustrating rate matching performed byseparating an encoded code block into a systematic part and a paritypart.

FIG. 3 illustrates an internal structure of a circular buffer.

FIGS. 4A and 4B are block diagrams for a polar code encoder.

FIGS. 5A and 5B illustrate the concept of channel combining and channelsplitting for channel polarization.

FIG. 6 illustrates N-th level channel combining for a polar code.

FIG. 7 illustrates an evolution of decoding paths in a list-L decodingprocess.

FIG. 8 illustrates the concept of selecting position(s) to whichinformation bit(s) are to be allocated in polar codes.

FIG. 9 illustrates puncturing and information bit allocation for Polarcodes.

FIGS. 10A and 10B illustrate the concept of a conventional cyclicredundancy check (CRC) code and a distributed CRC code.

FIG. 11 illustrates an encoding procedure and a decoding procedure in alegacy LTE system.

FIG. 12 illustrates a frame structure.

FIG. 13 illustrates the structure of a synchronization signal andphysical broadcast channel (PBCH) block (SSB).

FIG. 14 illustrates a signal processing procedure for a PBCH.

FIG. 15 illustrates a flowchart of PBCH transmission according toexamples of the present invention.

FIG. 16 illustrates bit error rate (BER) values of input bit indexes fora Polar code.

FIGS. 17A to 17C illustrate comparison of performance between bitpositions exemplified in the present disclosure.

FIG. 18 illustrates timing information bit fields included in asynchronization signal and PBCH block (SSB).

FIG. 19 is a block diagram illustrating elements of a transmittingdevice 10 and a receiving device 20 for implementing the presentinvention.

DETAILED DESCRIPTION

Reference will now be made in detail to the exemplary examples of thepresent invention, examples of which are illustrated in the accompanyingdrawings. The detailed description, which will be given below withreference to the accompanying drawings, is intended to explain exemplaryexamples of the present invention, rather than to show the only examplesthat can be implemented according to the invention. The followingdetailed description includes specific details in order to provide athorough understanding of the present invention. However, it will beapparent to those skilled in the art that the present invention may bepracticed without such specific details.

In some instances, known structures and devices are omitted or are shownin block diagram form, focusing on important features of the structuresand devices, so as not to obscure the concept of the present invention.The same reference numbers will be used throughout this specification torefer to the same or like parts.

The following techniques, apparatuses, and systems may be applied to avariety of wireless multiple access systems. Examples of the multipleaccess systems include a code division multiple access (CDMA) system, afrequency division multiple access (FDMA) system, a time divisionmultiple access (TDMA) system, an orthogonal frequency division multipleaccess (OFDMA) system, a single carrier frequency division multipleaccess (SC-FDMA) system, and a multicarrier frequency division multipleaccess (MC-FDMA) system. CDMA may be embodied through radio technologysuch as universal terrestrial radio access (UTRA) or CDMA2000. TDMA maybe embodied through radio technology such as global system for mobilecommunications (GSM), general packet radio service (GPRS), or enhanceddata rates for GSM evolution (EDGE). OFDMA may be embodied through radiotechnology such as institute of electrical and electronics engineers(IEEE) 802.11 (Wi-Fi), IEEE 802.16 (WiMAX), IEEE 802.20, or evolved UTRA(E-UTRA). UTRA is a part of a universal mobile telecommunications system(UMTS). 3rd generation partnership project (3GPP) long term evolution(LTE) is a part of evolved UMTS (E-UMTS) using E-UTRA. 3GPP LTE employsOFDMA in DL and SC-FDMA in UL. LTE-advanced (LTE-A) is an evolvedversion of 3GPP LTE. For convenience of description, it is assumed thatthe present invention is applied to 3GPP based communication system,e.g. LTE/LTE-A, NR. However, the technical features of the presentinvention are not limited thereto. For example, although the followingdetailed description is given based on a mobile communication systemcorresponding to a 3GPP LTE/LTE-A/NR system, aspects of the presentinvention that are not specific to 3GPP LTE/LTE-A/NR are applicable toother mobile communication systems.

In examples of the present invention described below, the expressionthat a device “assumes” may mean that a subject which transmits achannel transmits the channel in accordance with the corresponding“assumption”. This may also mean that a subject which receives thechannel receives or decodes the channel in a form conforming to the“assumption”, on the assumption that the channel has been transmittedaccording to the “assumption”.

In the present invention, a user equipment (UE) may be a fixed or mobiledevice. Examples of the UE include various devices that transmit andreceive user data and/or various kinds of control information to andfrom a base station (BS). The UE may be referred to as a terminalequipment (TE), a mobile station (MS), a mobile terminal (MT), a userterminal (UT), a subscriber station (SS), a wireless device, a personaldigital assistant (PDA), a wireless modem, a handheld device, etc. Inaddition, in the present invention, a BS generally refers to a fixedstation that performs communication with a UE and/or another BS, andexchanges various kinds of data and control information with the UE andanother BS. The BS may be referred to as an advanced base station (ABS),a node-B (NB), an evolved node-B (eNB), a base transceiver system (BTS),an access point (AP), a processing server (PS), etc. Particularly, a BSof a UTRAN is referred to as a Node-B, a BS of an E-UTRAN is referred toas an eNB, and a BS of a new radio access technology network is referredto as an gNB. Herein, for convenience of description, a base stationwill be referred to as a BS regardless of type or version ofcommunication technology.

In the present invention, a node refers to a fixed point capable oftransmitting/receiving a radio signal through communication with a UE.Various types of BSs may be used as nodes irrespective of the termsthereof. For example, a BS, a node B (NB), an e-node B (eNB), apico-cell eNB (PeNB), a home eNB (HeNB), a relay, a repeater, etc. maybe a node. In addition, the node may not be a BS. For example, the nodemay be a radio remote head (RRH) or a radio remote unit (RRU). The RRHor RRU generally has a lower power level than a power level of a BS.Since the RRH or RRU (hereinafter, RRH/RRU) is generally connected tothe BS through a dedicated line such as an optical cable, cooperativecommunication between RRH/RRU and the BS can be smoothly performed incomparison with cooperative communication between BSs connected by aradio line. At least one antenna is installed per node. The antenna maymean a physical antenna or mean an antenna port or a virtual antenna.

In the present invention, a cell refers to a prescribed geographicalarea to which one or more nodes provide a communication service.Accordingly, in the present invention, communicating with a specificcell may mean communicating with a BS or a node which provides acommunication service to the specific cell. In addition, a DL/UL signalof a specific cell refers to a DL/UL signal from/to a BS or a node whichprovides a communication service to the specific cell. A node providingUL/DL communication services to a UE is called a serving node and a cellto which UL/DL communication services are provided by the serving nodeis especially called a serving cell. Furthermore, channel status/qualityof a specific cell refers to channel status/quality of a channel orcommunication link formed between a BS or node which provides acommunication service to the specific cell and a UE. In the 3GPP basedcommunication system, the UE may measure DL channel state received froma specific node using cell-specific reference signal(s) (CRS(s))transmitted on a CRS resource and/or channel state information referencesignal(s) (CSI-RS(s)) transmitted on a CSI-RS resource, allocated byantenna port(s) of the specific node to the specific node.

Meanwhile, a 3GPP based communication system uses the concept of a cellin order to manage radio resources and a cell associated with the radioresources is distinguished from a cell of a geographic region.

A “cell” of a geographic region may be understood as coverage withinwhich a node can provide service using a carrier and a “cell” of a radioresource is associated with bandwidth (BW) which is a frequency rangeconfigured by the carrier. Since DL coverage, which is a range withinwhich the node is capable of transmitting a valid signal, and ULcoverage, which is a range within which the node is capable of receivingthe valid signal from the UE, depends upon a carrier carrying thesignal, the coverage of the node may be associated with coverage of the“cell” of a radio resource used by the node. Accordingly, the term“cell” may be used to indicate service coverage of the node sometimes, aradio resource at other times, or a range that a signal using a radioresource can reach with valid strength at other times.

Meanwhile, the 3GPP communication standards use the concept of a cell tomanage radio resources. The “cell” associated with the radio resourcesis defined by combination of downlink resources and uplink resources,that is, combination of DL CC and UL CC. The cell may be configured bydownlink resources only, or may be configured by downlink resources anduplink resources. If carrier aggregation is supported, linkage between acarrier frequency of the downlink resources (or DL CC) and a carrierfrequency of the uplink resources (or UL CC) may be indicated by systeminformation. For example, combination of the DL resources and the ULresources may be indicated by linkage of system information block type 2(SIB2). The carrier frequency may be the same as a center frequency ofeach cell or CC. A cell operating on a primary frequency may be referredto as a primary cell (Pcell) or PCC, and a cell operating on a secondaryfrequency may be referred to as a secondary cell (Scell) or SCC. Thecarrier corresponding to the Pcell on downlink will be referred to as adownlink primary CC (DL PCC), and the carrier corresponding to the Pcellon uplink will be referred to as an uplink primary CC (UL PCC). A Scellmeans a cell that may be configured after completion of radio resourcecontrol (RRC) connection establishment and used to provide additionalradio resources. The Scell may form a set of serving cells for the UEtogether with the Pcell in accordance with capabilities of the UE. Thecarrier corresponding to the Scell on the downlink will be referred toas downlink secondary CC (DL SCC), and the carrier corresponding to theScell on the uplink will be referred to as uplink secondary CC (UL SCC).Although the UE is in RRC-CONNECTED state, if it is not configured bycarrier aggregation or does not support carrier aggregation, a singleserving cell configured by the Pcell only exists.

3GPP based communication standards define DL physical channelscorresponding to resource elements carrying information derived from ahigher layer and DL physical signals corresponding to resource elementswhich are used by a physical layer but which do not carry informationderived from a higher layer. For example, a physical downlink sharedchannel (PDSCH), a physical broadcast channel (PBCH), a physicalmulticast channel (PMCH), a physical control format indicator channel(PCFICH), a physical downlink control channel (PDCCH), and a physicalhybrid ARQ indicator channel (PHICH) are defined as the DL physicalchannels, and a reference signal and a synchronization signal aredefined as the DL physical signals. A reference signal (RS), also calleda pilot, refers to a special waveform of a predefined signal known toboth a BS and a UE. For example, a cell-specific RS (CRS), a UE-specificRS (UE-RS), a positioning RS (PRS), and channel state information RS(CSI-RS) may be defined as DL RSs. Meanwhile, the 3GPP basedcommunication standards define UL physical channels corresponding toresource elements carrying information derived from a higher layer andUL physical signals corresponding to resource elements which are used bya physical layer but which do not carry information derived from ahigher layer. For example, a physical uplink shared channel (PUSCH), aphysical uplink control channel (PUCCH), and a physical random accesschannel (PRACH) are defined as the UL physical channels, and ademodulation reference signal (DM RS) for a UL control/data signal and asounding reference signal (SRS) used for UL channel measurement aredefined as the UL physical signals.

In the present invention, a physical downlink control channel (PDCCH), aphysical control format indicator channel (PCFICH), a physical hybridautomatic retransmit request indicator channel (PHICH), and a physicaldownlink shared channel (PDSCH) refer to a set of time-frequencyresources or resource elements (REs) carrying downlink controlinformation (DCI), a set of time-frequency resources or REs carrying acontrol format indicator (CFI), a set of time-frequency resources or REscarrying downlink acknowledgement (ACK)/negative ACK (NACK), and a setof time-frequency resources or REs carrying downlink data, respectively.In addition, a physical uplink control channel (PUCCH), a physicaluplink shared channel (PUSCH) and a physical random access channel(PRACH) refer to a set of time-frequency resources or REs carryinguplink control information (UCI), a set of time-frequency resources orREs carrying uplink data and a set of time-frequency resources or REscarrying random access signals, respectively. In the present invention,in particular, a time-frequency resource or RE that is assigned to orbelongs to PDCCH/PCFICH/PHICH/PDSCH/PUCCH/PUSCH/PRACH is referred to asPDCCH/PCFICH/PHICH/PDSCH/PUCCH/PUSCH/PRACH RE orPDCCH/PCFICH/PHICH/PDSCH/PUCCH/PUSCH/PRACH time-frequency resource,respectively. Therefore, in the present invention, PUCCH/PUSCH/PRACHtransmission of a UE is conceptually identical to UCI/uplink data/randomaccess signal transmission on PUSCH/PUCCH/PRACH, respectively. Inaddition, PDCCH/PCFICH/PHICH/PDSCH transmission of a BS is conceptuallyidentical to downlink data/DCI transmission on PDCCH/PCFICH/PHICH/PDSCH,respectively.

For terms and technologies which are not described in detail in thepresent invention, reference can be made to the standard document of3GPP LTE/LTE-A, for example, 3GPP TS 36.211, 3GPP TS 36.212, 3GPP TS36.213, 3GPP TS 36.321, and 3GPP TS 36.331 and the standard document of3GPP NR, for example, 3GPP TS 38.211, 3GPP TS 38.212, 3GPP TS 38.213,3GPP TS 38.214, 3GPP TS 38.300 and 3GPP TS 38.331. In addition, as topolar codes and the principle of encoding and decoding using the polarcodes, reference may be made to ‘E. Arikan, “Channel Polarization: AMethod for Constructing Capacity-Achieving Codes for SymmetricBinary-Input Memoryless Channels,” in IEEE Transactions on InformationTheory, vol. 55, no. 7, pp. 3051-3073, July 2009’.

As more communication devices have demanded higher communicationcapacity, there has been necessity of enhanced mobile broadband relativeto legacy radio access technology (RAT). In addition, massive machinetype communication for providing various services irrespective of timeand place by connecting a plurality of devices and objects to each otheris one main issue to be considered in future-generation communication.Further, a communication system design in which services/UEs sensitiveto reliability and latency are considered is under discussion. Theintroduction of future-generation RAT has been discussed by taking intoconsideration enhanced mobile broadband communication, massive MTC,ultra-reliable and low-latency communication (URLLC), and the like. Incurrent 3GPP, a study of the future-generation mobile communicationsystem after EPC is being conducted. In the present invention, thecorresponding technology is referred to as a new RAT (NR) or 5G RAT, forconvenience.

An NR communication system demands that much better performance than alegacy fourth generation (4G) system be supported in terms of data rate,capacity, latency, energy consumption, and cost. Accordingly, the NRsystem needs to make progress in terms of bandwidth, spectrum, energy,signaling efficiency, and cost per bit. NR needs to use efficientwaveforms in order to satisfy these requirements.

FIG. 1 illustrates a transport block processing procedure in anLTE/LTE-A system.

In order for a receiving side to correct errors that signals experiencein a channel, a transmitting side encodes information using a forwarderror correction code and then transmits the encoded information. Thereceiving side demodulates a received signal and decodes the errorcorrection code to thereby recover the information transmitted by thetransmitting side. In this decoding procedure, errors in the receivedsignal caused by a channel are corrected.

Data arrives at a coding block in the form of a maximum of two transportblocks every transmission time interval (TTI) in each DL/UL cell. Thefollowing coding steps may be applied to each transport block of theDL/UL cell:

-   -   cyclic redundancy check (CRC) attachment to a transport block;    -   code block segmentation and CRC attachment to a code block;    -   channel coding;    -   rate matching; and    -   code block concatenation.

Although various types of error correction codes are available, a turbocode has mainly been used in a legacy LTE/LTE-A system. The turbo codeis implemented by a recursive systematic convolution encoder and aninterleaver. For actual implementation of the turbo code, an interleaveris used to facilitate parallel decoding and quadratic polynomialpermutation (QPP) is a kind of interleaving. It is known that a QPPinterleaver maintains good performance only for a data block of aspecific size. It is known that performance of the turbo code increaseswith a larger data block size. In an actual communication system, a datablock of a predetermined size or larger is divided into a plurality ofsmaller data blocks and then is encoded, to facilitate actualimplementation of coding. The smaller data blocks are called codeblocks. While the code blocks are generally of the same size, one of thecode blocks may have a different size due to a limited size of the QPPinterleaver. Error correction coding is performed on each code block ofa predetermined interleaver size and then interleaving is performed toreduce the impact of burst errors that are generated during transmissionover a radio channel. The error-corrected and interleaved code block istransmitted by being mapped to an actual radio resource. The amount ofradio resources used for actual transmission is designated. Thus, theencoded code blocks are rate-matched to the amount of the radioresources. In general, rate matching is performed through puncturing orrepetition. For example, if the amount of radio resources, i.e., thenumber of transmission bits capable of being transmitted on the radioresources, is M and if a coded bit sequence, i.e., the number of outputbits of the encoder, is N, in which M is different from N, then ratematching is performed to match the length of the coded bit sequence toM. If M>N, then all or a part of bits of the coded bit sequence arerepeated to match the length of the rate-matched sequence to M. If M<N,then a part of the bits of the coded bit sequence is punctured to matchthe length of the rate-matched sequence to M and the punctured bits areexcluded from transmission.

Namely, in an LTE/LTE-A system, after data to be transmitted is encodedusing channel coding having a specific code rate (e.g., 1/3), the coderate of the data to be transmitted is adjusted through a rate-matchingprocedure consisting of puncturing and repetition. When the turbo codeis used as a channel code in the LTE/LTE-A system, a procedure ofperforming channel coding and rate-matching on each code block in thetransport block processing procedure as illustrated in FIG. 1 isillustrated in FIG. 2.

FIG. 2 is a block diagram illustrating rate matching performed byseparating an encoded code block into a systematic part and a paritypart.

As illustrated in FIG. 2, the mother code rate of an LTE/LTE-A turboencoder is 1/3. In order to obtain other code rates, if necessary,repetition or puncturing has to be performed, which are performed by arate matching module. The rate matching module consists of threeso-called sub-block interleavers for three output streams of the turboencoder and a bit selection and pruning part, which is realized by acircular buffer. The sub-block interleaver is based on a classicrow-column interleaver with 32 rows and length-32 intra-columnpermutation. The bits of each of the three streams are writtenrow-by-row into a matrix with 32 columns (number of rows depends onstream size). Dummy bits are padded to the front of each stream tocompletely fill the matrix. After column permutation, bits are read outfrom the matrix column-by-column.

FIG. 3 illustrates an internal structure of a circular buffer.

The circular buffer is the most important part of the rate matchingmodule, making it possible to perform puncturing and repetition of amother code. Referring to FIG. 2, the interleaved systematic bits arewritten into the circular buffer in sequence, with the first bit of theinterleaved systematic bit stream at the beginning of the buffer. Theinterleaved and interlaced parity bit streams are written into thebuffer in sequence, with the first bit of the stream next to the lastbit of the interleaved systematic bit stream. Coded bits (depending oncode rate) are read out serially from a certain starting point specifiedby redundancy version (RV) points in the circular buffer. If the codedbits reaches the end of the circular buffer and more coded bits areneeded for transmission (in the case of a code rate smaller than 1/3), atransmitting device wraps around and continues at the beginning of thecircular buffer.

HARQ, which stands for Hybrid ARQ, is an error correction mechanismbased on retransmission of packets, which are detected with errors. Thetransmitted packet arrives at a receiving device after a certainpropagation delay. The receiving device produces ACK for the case oferror-free transmission or NACK for the case of detection of someerrors. ACK/NACK is produced after some processing time and sent back tothe transmitting device and arrives at the transmitting device after apropagation delay. In the case of NACK, after a certain processing delayin the transmitting device, a desired packet will be sent again. Bits,which are read out from the circular buffer and sent throughretransmission, are different and depend on the position of the RV.There are four RVs (0, 1, 2, and 3), which define the position of astarting point at which the bits are read out from the circular buffer.Referring to FIG. 3, with the progressing number of retransmissions, theRV becomes higher and therefore fewer systematic bits and more paritybits are read out from the circular buffer for retransmission.

NR provides higher speeds and better coverage than current 4G. NRoperates in a high frequency band and is required to offer speeds of upto 1 Gb/s for tens of connections or tens of Mb/s for tens of thousandsof connections. To meet requirements of such an NR system, introductionof a more evolved coding scheme than a legacy coding scheme is underdiscussion. Since data communication arises in an incomplete channelenvironment, channel coding plays an important role in achieving ahigher data rate for fast and error-free communication. A selectedchannel code needs to provide superior block error ratio (BLER)performance for block lengths and code rates of a specific range.Herein, BLER is defined as the ratio of the number of erroneous receivedblocks to the total number of sent blocks. In NR, low calculationcomplexity, low latency, low cost, and higher flexibility are demandedfor a coding scheme. Furthermore, reduced energy per bit and improvedregion efficiency are needed to support a higher data rate. Use examplesfor NR networks are enhanced mobile broadband (eMBB), massive Internetof things (IoT), and ultra-reliable and low latency communication(URLLC). eMBB covers Internet access with high data rates to enable richmedia applications, cloud storage and applications, and augmentedreality for entertainment. Massive IoT applications include dense sensornetworks for smart homes/buildings, remote health monitoring, andlogistics tracking. URLLC covers critical applications that demandultra-high reliability and low latency, such as industrial automation,driverless vehicles, remote surgery, and smart grids.

Although many coding schemes with high capacity performance at largeblock lengths are available, many of these coding schemes do notconsistently exhibit excellent good performance in a wide range of blocklengths and code rates. However, turbo codes, low-density parity check(LPDC) codes, and polar codes show promising BLER performance in a widerange of coding rates and code lengths and hence are considered to beused in the NR system. As demand for various cases such as eMBB, massiveIoT, and URLLC has increased, a coding scheme providing greater channelcoding efficiency than in turbo codes is needed. In addition, increasein a maximum number of subscribers capable of being accommodated by achannel, i.e., increase in capacity, has been required.

Polar codes are codes providing a new framework capable of solvingproblems of legacy channel codes and were invented by Arikan at BilkentUniversity (reference: E. Arikan, “Channel Polarization: A Method forConstructing Capacity-Achieving Codes for Symmetric Binary-InputMemoryless Channels,” in IEEE Transactions on Information Theory, vol.55, no. 7, pp. 3051-3073, July 2009). Polar codes are the firstcapacity-achieving codes with low encoding and decoding complexities,which were proven mathematically. Polar codes outperform the turbo codesin large block lengths while no error flow is present. Hereinafter,channel coding using the polar codes is referred to as polar coding.

Polar codes are known as codes capable of achieving the capacity of agiven binary discrete memoryless channel. This can be achieved only whena block size is sufficiently large. That is, polar codes are codescapable of achieving the capacity of a channel if the size N of thecodes infinitely increases. Polar codes have low encoding and decodingcomplexity and may be successfully decoded. Polar codes are a sort oflinear block error correction codes. Multiple recursive concatenationsare basic building blocks for the polar codes and are bases for codeconstruction. Physical conversion of channels in which physical channelsare converted into virtual channels occurs and such conversion is basedon a plurality of recursive concatenations. If multiple channels aremultiplied and accumulated, most of the channels may become better orworse. The idea underlying polar codes is to use good channels. Forexample, data is sent through good channels at rate 1 and data is sentthrough bad channels at rate 0. That is, through channel polarization,channels enter a polarized state from a normal state.

FIGS. 4A and 4B are block diagrams for a polar code encoder.

FIG. 4A illustrates a base module of a polar code, particularly, firstlevel channel combining for polar coding. In FIG. 4A, W₂ denotes anentire equivalent channel obtained by combining two binary-inputdiscrete memoryless channels (B-DMCs), Ws. Herein, u₁ and u₂ arebinary-input source bits and y₁ and y₂ are output coded bits. Channelcombining is a procedure of concatenating the B-DMCs in parallel.

FIG. 4B illustrates a base matrix F for the base module. Thebinary-input source bits u₁ and u₂ input to the base matrix F and theoutput coded bits x₁ and x₂ of the base matrix F have the followingrelationship.

$\begin{matrix}{{\left\lbrack {u_{1}\mspace{20mu} u_{2}} \right\rbrack\begin{bmatrix}1 & 0 \\1 & 1\end{bmatrix}} = \left\lbrack {x_{1}\mspace{20mu} x_{2}} \right\rbrack} & {{Equation}\mspace{14mu} 1}\end{matrix}$

The channel W₂ may achieve symmetric capacity I(W) which is a highestrate. In the B-DMC W, symmetric capacity is an important parameter whichis used to measure a rate and is a highest rate at which reliablecommunication can occur over the channel W. The B-DMC may be defined asfollows.

$\begin{matrix}{{I(W)} = {\sum\limits_{y \in Y}^{\;}{\sum\limits_{x \in X}{{1/2}{W\left( y \middle| x \right)}\log\frac{w\left( y \middle| x \right)}{{{1/2}{w\left( y \middle| 0 \right)}} + {{1/2}{w\left( y \middle| 1 \right)}}}}}}} & {{Equation}\mspace{14mu} 2}\end{matrix}$

It is possible to synthesize or create a second set of N binary inputchannels out of N independent copies of a given B-DMC W and the channelshave the properties {W_(N) ^((i)): 1≤i≤N}. If N increases, there is atendency for a part of the channels to have capacity approximating to 1and for the remaining channels to have capacity approximating to 0. Thisis called channel polarization. In other words, channel polarization isa process of creating a second set of N channels {W_(N) ^((i)): 1≤i≤N}using N independent copies of a given B-DMC W. The effect of channelpolarization means that, when N increases, all symmetric capacity terms{I(W_(N) ^((i)))} tend towards 0 or 1 for all except a vanishingfraction of indexes i. In other words, the concept behind channelpolarization in the polar codes is transforming N copies (i.e., Ntransmissions) of a channel having a symmetric capacity of I(W) (e.g.,additive white Gaussian noise channel) into extreme channels of capacityclose to 1 or 0. Among the N channels, an I(W) fraction will be perfectchannels and an 1−I(W) fraction will be completely noise channels. Then,information bits are transmitted only through good channels and bitsinput to the other channels are frozen to 1 or 0. The amount of channelpolarization increases along with a block length. Channel polarizationconsists of two phases: channel combining phase and channel splittingphase.

FIGS. 5A and 5B illustrate the concept of channel combining and channelsplitting for channel polarization. As illustrated in FIGS. 5A and 5B,when N copies of an original channel W are properly combined to create avector channel W_(vec) and then are split into new polarized channels,the new polarized channels are categorized into channels having capacityC(W)=1 and channels having C(W)=0 if N is sufficiently large. In thiscase, since bits passing through the channels having the channelcapacity C(W))=1 are transmitted without error, it is better to transmitinformation bits therethrough and, since bits passing through thechannels having capacity C(W)=0 cannot transport information, it isbetter to transport frozen bits, which are meaningless bits,therethrough.

Referring to FIGS. 5A and 5B, copies of a given B-DMC W are combined ina recursive manner to output a vector channel W_(vec) given byX_(N)→Y_(N), where N=2^(n) and n is an integer equal to or greater than0. Recursion always begins at the 0th level and W₁=W. If n is 1 (n=1),this means the first level of recursion in which two independent copiesof W₁ are combined. If the above two copies are combined, a channel W₂:X₂→Y₂ is obtained. A transitional probability of this new channel W₂ maybe represented by the following equation.W ₂(y ₁ ,y ₂ |u ₁ ,u ₂)=W(y ₁ |u ₁ ⊕u ₂)W(y ₁ |u ₂)  Equation 3

If the channel W₂ is obtained, two copies of the channel W₂ are combinedto obtain a single copy of a channel W₄. Such recursion may berepresented by W₄: X₄→Y₄ having the following transitional probability.W ₄(y ₁ ⁴ |u ₁ ⁴)=W ₂(y ₁ ² |u ₁ ⊕u ₂ ,u ₃ ⊕u ₄)W ₂(y ₃ ⁴ |u ₂ ,u₄)  Equation 4

In FIG. 5A, G_(N) is a size-N generator matrix. G₂ corresponds to thebase matrix F illustrated in FIG. 4B. G₄ may be represented by thefollowing matrix.

$\begin{matrix}{G_{4} = {{{\begin{bmatrix}1 & 0 & 0 & 0 \\0 & 0 & 1 & 0 \\0 & 1 & 0 & 0 \\0 & 0 & 0 & 1\end{bmatrix}\begin{bmatrix}1 & 0 \\1 & 1\end{bmatrix}}\,^{\otimes 2}} = \begin{bmatrix}1 & 0 & 0 & 0 \\1 & 0 & 1 & 0 \\1 & 1 & 0 & 0 \\1 & 1 & 1 & 1\end{bmatrix}}} & {{Equation}\mspace{14mu} 5}\end{matrix}$

Herein,

denotes the Kronecker product,

^(n)=A

for all n≥1, and

=1.

The relationship between input u^(N) ₁ to G_(N) and output x^(N) ₁ ofG_(N) of FIG. 5B may be represented as x^(N) ₁=u^(N) ₁G_(N), where x^(N)₁={x₁, . . . , x_(N)}, u^(N) ₁={u₁, . . . , u_(N)}

When N B-DMCs are combined, each B-DMC may be expressed in a recursivemanner. That is, G_(N) may be indicated by the following equation.G _(N) =B _(N) F ^(Wn)  Equation 6

Herein, N=2^(n), n≥1,

=F

, and

=1. B_(N) is a permutation matrix known as a bit-reversal operation andB_(N)=R_(N)(I₂

B_(N/2)) and may be recursively computed. I₂ is a 2-dimensional identitymatrix and this recursion is initialized to B₂=I₂. R_(N) is abit-reversal interleaver and is used to map an input s^(N) ₁={s₁, . . ., s_(N)} to an output x^(N) ₁={s₁, s₃, . . . , s_(N−1), s₂, . . . ,s_(N)}. The bit-reversal interleaver may not be included in atransmitting side. The relationship of Equation is illustrated in FIG.6.

FIG. 6 illustrates N-th level channel combining for a polar code.

A process of defining an equivalent channel for specific input aftercombining N B-DMCs Ws is called channel splitting. Channel splitting maybe represented as a channel transition probability indicated by thefollowing equation.

$\begin{matrix}{{W_{N}^{i}\left( {y_{1}^{N},\left. u_{1}^{i - 1} \middle| u_{i} \right.} \right)} = {\sum\limits_{u_{i + 1}^{N}}{\frac{1}{2^{N - 1}}{W_{N}\left( y_{1}^{N} \middle| u_{1}^{N} \right)}}}} & {{Equation}\mspace{14mu} 7}\end{matrix}$

Channel polarization has the following characteristics:C(W ⁻)+C(W ⁺)=2C(W),  Conservation:C(W ⁻)≤C(W)≤C(W ⁺).  Extremization:

When channel combining and channel splitting are performed, thefollowing theorem may be obtained.

Theorem: For any B-DMC W, channels {W_(N) ^((i))} are polarized in thefollowing sense. For any fixed δ∈{0, 1}, as N goes to infinity throughpowers of 2, the fraction of indexes i∈{1, . . . , N} for channelcapacity I(W_(N) ^((i)))∈(1−δ, 1] goes to I(W) and the faction of i forchannel capacity I(W_(N) ^((i)))∈[0, δ) goes to 1−I(W). Hence, if N→∞,then channels are perfectly noisy or are polarized free of noise. Thesechannels can be accurately recognized by the transmitting side.Therefore, bad channels are fixed and non-fixed bits may be transmittedon good channels.

That is, if the size N of polar codes is infinite, a channel has muchnoise or is free of noise, with respect to a specific input bit. Thishas the same meaning that the capacity of an equivalent channel for aspecific input bit is divided into 0 or I(W).

Inputs of a polar encoder are divided into bit channels to whichinformation data is mapped and bit channels to which the informationdata is not mapped. As described earlier, according to the theorem ofthe polar code, if a codeword of the polar code goes to infinity, theinput bit channels may be classified into noiseless channels and noisechannels. Therefore, if information is allocated to the noiseless bitchannels, channel capacity may be obtained. However, in actuality, acodeword of an infinite length cannot be configured, reliabilities ofthe input bit channels are calculated and data bits are allocated to theinput bit channels in order of reliabilities. In the present invention,bit channels to which data bits are allocated are referred to as goodbit channels. The good bit channels may be input bit channels to whichthe data bits are mapped. Bit channels to which data is not mapped arereferred to as frozen bit channels. A known value (e.g., 0) is input tothe frozen bit channels and then encoding is performed. Any values whichare known to the transmitting side and the receiving side may be mappedto the frozen bit channels. When puncturing or repetition is performed,information about the good bit channels may be used. For example,positions of codeword bits (i.e., output bits) corresponding topositions of input bits to which information bits are not allocated maybe punctured.

A decoding scheme of the polar codes is a successive cancellation (SC)decoding scheme. The SC decoding scheme obtains a channel transitionprobability and then calculates a likelihood ratio (LLR) of input bitsusing the channel transition probability. In this case, the channeltransition probability may be calculated in a recursive form if channelcombining and channel splitting procedures use characteristics of therecursive form. Therefore, a final LLR value may also be calculated inthe recursive form. First, a channel transition probability W_(N)^((i))(y₁ ^(N), u₁ ^(i−1)|u₁) of an input bit u_(i) may be obtained asfollows. u₁ ^(i) may be split into odd indexes and even indexes asexpressed as u_(1,o) ^(i), u_(1,e) ^(i), respectively. The channeltransition probability may be indicated by the following equations.

$\begin{matrix}{{{W_{2N}^{({{2i} - 1})}\left( {y_{1}^{2N},\left. u_{1}^{{2i} - 1} \middle| u_{{2i} - 1} \right.} \right)} = {{\sum\limits_{u_{2i}^{2N}}{\frac{1}{2^{{2N} - 1}}{W_{2N}\left( y_{1}^{2N} \middle| u_{1}^{2N} \right)}}} = {{\sum\limits_{u_{{2i},o}^{2N},u_{{2i},e}^{2N}}{\frac{1}{2^{{2N} - 1}}{W_{N}\left( y_{1}^{N} \middle| {u_{1,o}^{2N} \oplus u_{i,e}^{2N}} \right)}{W_{N}\left( y_{N + 1}^{2N} \middle| u_{1,e}^{2N} \right)}}} = {{\sum\limits_{u_{2i}}{\frac{1}{2}{\sum\limits_{u_{{{2i} + 1},e}^{2N}}^{\;}{\frac{1}{2^{N - 1}}{{W_{N}\left( y_{N + 1}^{2N} \middle| u_{1,e}^{2N} \right)} \cdot {\sum\limits_{u_{{{2i} + 1},o}^{2N}}^{\;}{\frac{1}{2^{N - 1}}{W_{N}\left( y_{1}^{N} \middle| {u_{1,o}^{2N} \oplus u_{i,e}^{2N}} \right)}}}}}}}} = {\sum\limits_{u_{2i}}{\frac{1}{2}{{W_{N}^{(i)}\left( {y_{1}^{N},\left. {u_{1,o}^{{2i} - 2} \oplus u_{i,e}^{{2i} - 2}} \middle| {u_{{2i} - 1} \oplus u_{2i}} \right.} \right)} \cdot {W_{N}^{(i)}\left( {y_{N + 1}^{2N},\left. u_{1,e}^{{2i} - 2} \middle| u_{2i} \right.} \right)}}}}}}}}\mspace{20mu}{{{where}\mspace{14mu}{W_{N}^{(i)}\left( {y_{1}^{N},\left. u_{1}^{i - 1} \middle| u_{i} \right.} \right)}} = {\sum\limits_{u_{i + 1}^{N}}{\frac{1}{2^{N + i}}{{W_{N}\left( y_{1}^{N} \middle| u_{1}^{N} \right)}.}}}}} & {{Equation}\mspace{14mu} 8} \\{{W_{2N}^{({2i})}\left( {y_{1}^{2N},\left. u_{1}^{{2i} - 1} \middle| u_{2i} \right.} \right)} = {{\sum\limits_{u_{{2i} + 1}^{2N}}{\frac{1}{2^{{2N} - 1}}{W_{2N}\left( y_{1}^{2N} \middle| u_{1}^{2N} \right)}}} = {{\sum\limits_{u_{{{2i} + 1},o}^{2N},u_{{{2i} + 1},e}^{2N}}{\frac{1}{2^{{2N} - 1}}{W_{N}\left( y_{1}^{N} \middle| {u_{1,o}^{2N} \oplus u_{i,e}^{2N}} \right)}{W_{N}\left( y_{N + 1}^{2N} \middle| u_{1,e}^{2N} \right)}}} = {{\frac{1}{2}{\sum\limits_{u_{{{2i} + 1},e}^{2N}}^{\;}{\frac{1}{2^{N - 1}}{{W_{N}\left( y_{N + 1}^{2N} \middle| u_{1,e}^{2N} \right)} \cdot {\sum\limits_{u_{{{2i} + 1},o}^{2N}}^{\;}{\frac{1}{2^{N - 1}}{W_{N}\left( y_{1}^{N} \middle| {u_{1,o}^{2N} \oplus u_{i,e}^{2N}} \right)}}}}}}} = {\frac{1}{2}{{W_{N}^{(i)}\left( {y_{1}^{N},\left. {u_{1,o}^{{2i} - 2} \oplus u_{i,e}^{{2i} - 2}} \middle| {u_{{2i} - 1} \oplus u_{2i}} \right.} \right)} \cdot {W_{N}^{(i)}\left( {y_{N + 1}^{2N},\left. u_{1,e}^{{2i} - 2} \middle| u_{2i} \right.} \right)}}}}}}} & {{Equation}\mspace{14mu} 9}\end{matrix}$

A polar decoder retrieves information and generates an estimateu{circumflex over ( )}^(N) ₁ of u^(N) ₁ using values (e.g., receptionbits, frozen bits, etc.) known for the polar codes. The LLR is definedas follows.

$\begin{matrix}{{L_{N}^{(i)}\left( {y_{1}^{N},u_{1}^{i - 1}} \right)} = \frac{W_{N}^{(i)}\left( {y_{1}^{N},{\left. u_{1}^{i - 1} \middle| u_{i} \right. = 0}} \right)}{W_{N}^{(i)}\left( {y_{1}^{N},{\left. u_{1}^{i - 1} \middle| u_{i} \right. = 1}} \right)}} & {{Equation}\mspace{14mu} 10}\end{matrix}$

The LLR may be recursively calculated as follows.

$\begin{matrix}{{{L_{N}^{({{2i} - 1})}\left( {y_{1}^{N},{\hat{u}}_{1}^{{2i} - 2}} \right)} = \frac{\begin{matrix}{{L_{N/2}^{(i)}\left( {y_{1}^{N/2},{{\hat{u}}_{1,o}^{{2i} - 2} \oplus {\hat{u}}_{1,e}^{{2i} - 2}}} \right)} \cdot} \\{{L_{N/2}^{(i)}\left( {y_{{N/2} + 1}^{N},{\hat{u}}_{1,e}^{{2i} - 2}} \right)} + 1}\end{matrix}}{{L_{N/2}^{(i)}\left( {y_{1}^{N/2},{{\hat{u}}_{1,o}^{{2i} - 2} \oplus {\hat{u}}_{1,e}^{{2i} - 2}}} \right)} + {L_{N/2}^{(i)}\left( {y_{{N/2} + 1}^{N},{\hat{u}}_{1,e}^{{2i} - 2}} \right)}}}{{L_{N}^{({2i})}\left( {y_{1}^{N},{\hat{u}}_{1}^{{2i} - 2}} \right)} = {\left\lbrack {L_{N/2}^{(i)}\left( {y_{1}^{N/2},{{\hat{u}}_{1,o}^{{2i} - 2} \oplus {\hat{u}}_{1,e}^{{2i} - 2}}} \right)} \right\rbrack^{1 - {2{\hat{u}}_{{2i} - 1}}} \cdot {L_{N/2}^{(i)}\left( {y_{{N/2} + 1}^{N},{\hat{u}}_{1,e}^{{2i} - 2}} \right)}}}} & {{Equation}\mspace{14mu} 11}\end{matrix}$

Recursive calculation of LLRs is traced back to a code length of 1 withan LLR L⁽¹⁾ ₁(y_(i))=W(y_(i)|0)/W(y_(i)|1). L⁽¹⁾ ₁(y_(i)) is softinformation observed from a channel.

The complexity of a polar encoder and an SC decoder varies with thelength N of polar codes and is known as having O(N log N). Assuming thatK input bits are used for a length-N polar code, a coding rate becomesN/K. If a generator matrix of a polar encoder of a data payload size Nis G_(N), an encoded bit may be represented as x^(N) ₁=u^(N) ₁G_(N). Itis assumed that K bits out of u^(N) ₁ correspond to payload bits, a rowindex of G_(N) corresponding to the payload bits is i, and a row indexof G_(N) corresponding to (N−K) bits is F. A minimum distance of thepolar codes may be given as d_(min)(C)=min_(i∈I)2^(wt(i)), where wt(i)is the number of 1s within binary extension of i and i=0, 1, . . . ,N−1.

SC list (SCL) decoding is an extension of a basic SC decoder. In thistype of decoder, L decoding paths are simultaneously considered in eachdecoding stage. Herein, L is an integer. In other words, in the case ofthe polar codes, a list-L decoding algorithm is an algorithm forsimultaneously tracking L paths in a decoding process.

FIG. 7 illustrates an evolution of decoding paths in a list-L decodingprocess. For convenience of description, it is assumed that the numberof bits that should be determined is n and all bits are not frozen. If alist size L is 4, each level includes at most 4 nodes with paths thatcontinue downward. Discontinued paths are expressed by dotted lines inFIG. 7. A process in which decoding paths evolve in list-L decoding willnow be described with reference to FIG. 7. i) If list-L decoding isstarted, the first unfrozen bit may be either 0 or 1. ii) list-Ldecoding continues. The second unfrozen bits may be either 0 or 1. Sincethe number of paths is not greater than L=4, pruning is not needed yet.iii) Consideration of all options for the first bit (i.e., a bit of thefirst level), the second bit (i.e. a bit of the second level), and thethird bit (i.e., a bit of the third level) results in 8 decoding pathswhich are excessive because L=4. iv) the 8 decoding paths are pruned toL(=4) promising paths. v) 4 active paths continue by considering twooptions of the fourth unfrozen bit. In this case, the number of paths isdoubled, i.e., 8 paths which are excessive because L=4. vi) The 8 pathsare pruned back to L(=4) best paths. In the example of FIG. 7, 4candidate codewords 0100, 0110, 0111, and 1111 are obtained and one ofthe codewords is determined to be a codeword most similar to an originalcodeword. In a similar manner to a normal decoding process, for example,in a pruning process or a process of determining a final codeword, apath in which the sum of LLR absolute values is largest may be selectedas a survival path. If a CRC is present, the survival path may beselected through the CRC.

Meanwhile, CRC-aided SCL decoding is SCL decoding using CRC and improvesthe performance of polar codes. CRC is the most widely used technique inerror detection and error correction in the field of information theoryand coding. For example, if an input block of an error correctionencoder has K bits and the length of information bits is k, and thelength of CRC sequences is m bits, then K=k+m. CRC bits are a part ofsource bits for an error correction code. If the size of channel codesused for encoding is N, a code rate R is defined as R=K/N. CRC aided SCLdecoding serves to detect an errorless path while a receiving deviceconfirms a CRC code with respect to each path. An SCL decoder outputscandidate sequences to a CRC detector. The CRC detector feeds back acheck result in order to aid in determining a codeword.

Although complicated as compared with an SC algorithm, SCL decoding orCRC aided SCL decoding has an advantage of excellent decodingperformance. For more details of a list-X decoding algorithm of thepolar codes, refer to ‘I. Tal and A. Vardy, “List decoding of polarcodes,” in Proc. IEEE Int. Symp. Inf. Theory, pp. 1-5, July 2011’.

In the polar codes, code design is independent of a channel and hence isnot versatile for mobile fading channels. In addition, the polar codeshave a disadvantage of limited application because the codes haverecently been introduced and have not grown yet. That is, polar codingproposed up to now has many parts that have not been defined to apply toa wireless communication system. Therefore, the present inventionproposes a polar coding method suitable for the wireless communicationsystem.

FIG. 8 illustrates the concept of selecting position(s) to whichinformation bit(s) are to be allocated in polar codes.

In FIG. 8, it is assumed that the size N of mother codes is 8, i.e., thesize N of polar codes is 8, and a code rate is 1/2.

In FIG. 8, C(W_(i)) denotes the capacity of a channel W_(i) andcorresponds to the reliability of channels that input bits of a polarcode experience. When channel capacities corresponding to input bitpositions of the polar code are as illustrated in FIG. 8, reliabilitiesof the input bit positions are ranked as illustrated in FIG. 8. Totransmit data at a code rate of 1/2, a transmitting device allocates 4bits constituting the data to 4 input bit positions having high channelcapacities among 8 input bit positions (i.e., input bit positionsdenoted as U₄, U₆, U₇, and U₈ among input bit positions U₁ to U₈ of FIG.8) and freezes the other input bit positions. A generator matrix G₈corresponding to the polar code of FIG. 8 is as follows. The generatormatrix G₈ may be acquired based on Equation 6.

$\begin{matrix}{G_{8} = \begin{bmatrix}1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 \\1 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\1 & 1 & 1 & 1 & 0 & 0 & 0 & 0 \\1 & 0 & 0 & 0 & 1 & 0 & 0 & 0 \\1 & 1 & 0 & 0 & 1 & 1 & 0 & 0 \\1 & 0 & 1 & 0 & 1 & 0 & 1 & 0 \\1 & 1 & 1 & 1 & 1 & 1 & 1 & 1\end{bmatrix}} & {{Equation}\mspace{14mu} 12}\end{matrix}$

The input bit positions denoted as U₁ to U₈ of FIG. 8 correspond one byone to rows from the highest row to the lowest row of G₈. Referring toFIG. 8, it may be appreciated that the input bit corresponding to U₈affects all output coded bits. On the other hand, it may be appreciatedthat the input bit corresponding to U₁ affects only Y₁ among the outputcoded bits. Referring to Equation 12, when binary-input source bits U₁to U₈ are multiplied by G₈, a row in which the input bits appear at alloutput bits is the lowest row [1, 1, 1, 1, 1, 1, 1, 1] in which allelements are 1, among rows of G₈. Meanwhile, a row in which thebinary-input source bits appears at only one output bit is a row inwhich one element is 1 among the rows of G₈, i.e., a row [1, 0, 0, 0, 0,0, 0, 0] in which a row weight is 1. Similarly, it may be appreciatedthat a row in which a row weight is 2 reflects input bits correspondingto the row in two output bits. Referring to FIG. 8 and Equation 12, U₁to U₈ correspond one by one to the rows of G₈ and bit indexes fordistinguishing between input positions of U₁ to U₈, i.e., bit indexesfor distinguishing between the input positions, may be assigned to therows of G₈.

Hereinafter, for Polar codes, it may be assumed that bit indexes from 0to N−1 are sequentially allocated to rows of G_(N) starting from thehighest row having the smallest row weight with respect to N input bits.For example, referring to FIG. 8, a bit index 0 is allocated to theinput position of U₁, i.e., the first row of G₈ and a bit index 7 isallocated to the input position of U₈, i.e., the last row of G₈.However, since the bit indexes are used to indicate input positions ofthe polar code, a scheme different from the above allocation scheme maybe used. For example, bit indexes from 0 to N−1 may be allocated staringfrom the lowest row having the largest row weight.

In the case of output bit indexes, as illustrated in FIG. 8 and Equation12, it may be assumed that bit indexes from 0 to N−1 or bit indexes from1 to N are assigned to columns from the first column having the largestcolumn weight to the last column having the smallest column weight amongcolumns of G_(N).

In Polar codes, setting of information bits and frozen bits is one ofthe most important elements in the configuration and performance of thepolar code. That is, determination of ranks of input bit positions maybe an important element in the performance and configuration of thepolar code. For Polar codes, bit indexes may distinguish input or outputpositions of the polar code. In the present invention, a sequenceobtained by enumerating reliabilities of bit positions in ascending ordescending order are referred to as a bit index sequence. That is, thebit index sequence represents reliabilities of input or output bitpositions of the polar code in ascending or descending order. Atransmitting device inputs information bits to input bits having highreliabilities based on the input bit index sequence and performsencoding using the polar code. A receiving device may discern inputpositions to which information bits are allocated or input positions towhich frozen bits are allocated, using the same or corresponding inputbit index sequence. That is, the receiving device may perform polardecoding using an input bit index sequence which is identical to orcorresponds to an input bit index sequence used by the transmittingdevice and using a corresponding polar code. In the followingdescription, it may be assumed that an input bit index sequence ispredetermined so that information bit(s) may be allocated to input bitposition(s) having high reliabilities. In the present disclosure, theinput bit index sequence is also called a Polar sequence.

FIG. 9 illustrates puncturing and information bit allocation for polarcodes. In FIG. 9, F denotes a frozen bit, D denotes an information bit,and 0 denotes a skipping bit.

Among coded bits, the case in which an information bit is changed to afrozen bit may occur according to an index or position of a puncturedbit. For example, if output coded bits for a mother code of N=8 shouldbe punctured in order of Y8, Y7, Y6, Y4, Y5, Y3, Y2, and Y1 and a targetcode rate is 1/2, then Y8, Y7, Y6, and Y4 are punctured, U8, U7, U6, andU4 connected only to Y8, Y7, Y6, and Y4 are frozen to 0, and these inputbits are not transmitted, as illustrated in FIG. 9. An input bit changedto a frozen bit by puncturing of a coded bit is referred to as askipping bit or a shortening bit and a corresponding input position isreferred to as a skipping position or a shortening position. Shorteningis a rate matching method of inserting a known bit into an input bitposition connected to a position of an output bit desired to betransmitted while maintaining the size of input information (i.e., thesize of information blocks). Shortening is possible starting from inputcorresponding to a column in which a column weight is 1 in a generatormatrix G_(N) and next shortening may be performed with respect to inputcorresponding to a column in which a column weight is 1 in a remainingmatrix from which a column and row in which a column weight is 1 areremoved. To prevent all information bits from being punctured, aninformation bit that should have been allocated to an information bitposition may be reallocated in order of a high reliability within a setof frozen bit positions.

In the case of the polar code, decoding may be generally performed inthe following order.

1. Bit(s) having low reliabilities are recovered first. Althoughreliability differs according to the structure of a decoder, since aninput index in an encoder (hereinafter, an encoder input bit index orbit index) having a low value usually has a low reliability, decoding isgenerally performed staring from a low encoder input bit index.

2. When there is a known bit for a recovered bit, the known bit is usedtogether with the recovered bit or the process of 1 is omitted and aknown bit for a specific input bit position is immediately used, therebyrecovering an information bit, which is an unknown bit. The informationbit may be a source information bit (e.g., a bit of a transport block)or a CRC bit.

FIGS. 10A and 10B illustrate the concept of a conventional CRC code anda distributed CRC code. FIG. 10A illustrates conventional CRC and FIG.10B illustrates distributed CRC.

In Polar codes, a CRC-aided list (CAL) decoding method is widely useddue to superior decoding performance thereof. According to the CALdecoding method, L (where, L is a positive integer) candidateinformation bit sequences {u_(i): i−1, . . . , L} are first decoded.Then, CRC-CHECK for the candidate information bit sequences is performedso that a candidate sequence passing CRC-CHECK is selected as a decodedinformation bit sequence.

Generally, CRC bits are positioned after information bits as illustratedin FIG. 10A. Therefore, a decoder generally decodes all information bitsand then performs CRC-CHECK for the decoded information bits. However,distributed CRC has recently been proposed to improve a decoding speedof the CAL decoding method. In distributed CRC, CRC bits areappropriately distributed over information bits as illustrated in FIG.10B. If distributed CRC is used as illustrated in FIG. 10B, a decodermay decode a part (e.g., an information sub-block of K₁ bits) ofinformation bits and a part (e.g., a CRC block of J₁ bits) in a CALdecoding process and perform CRC-CHECK using the decoded blocks. In thiscase, if CRC-CHECK for all the L candidate information bit sequencesfails, the decoder may declare an error and stop decoding. That is, whendistributed CRC is used, it is possible perform early termination ofdecoding in the CAL decoding process. If decoding of a received signalcan be terminated early, a receiving device may rapidly determinewhether the received signal is a signal therefor, and thus the receivingdevice increases speed for discovering a signal thereof. Furthermore,since an error of the received signal can be quickly discovered,retransmission for the received signal or next transmission followingthe received signal may be rapidly performed.

FIG. 11 illustrates an encoding procedure and a decoding procedure in alegacy LTE system. Particularly, FIG. 11(a) illustrates an encodingprocedure including a scrambling process and FIG. 11(b) illustrates adecoding procedure including a descrambling process.

Referring to FIG. 11(a), a transmitting device inserts a CRC code into atransport block or a code block (S1101 a) and scrambles obtained inputbits using a scrambling sequence (S1103 a). The transmitting devicechannel-encodes the scrambled input bits (S1105 a) to generate codedbits and channel-interleaves the coded bits (S1107 a). Referring to FIG.11(b), a receiving device obtains coded bits from received bits based ona channel interleaving pattern applied in the encoding procedure or achannel interleaving pattern corresponding thereto (S1107 b) andchannel-decodes the coded bits (S1105 b) to obtain scrambled bits. Thereceiving device descrambles the scrambled bits using a scramblingsequence (S1103 b) to obtain a sequence of decoded bits (hereinafter, adecoded bit sequence). The receiving device checks whether errors occurin the decoded bit sequence using CRC bits in the decoded bit sequence(S1101 b). If CRC for the decoded bit sequence fails, the receivingdevice determines that decoding of a received signal has failed. If CRCfor the decoded bit sequence is successful, the receiving devicedetermines that the decoding procedure has succeeded and may obtain thetransport block or the code block by eliminating the CRC bits from thedecoded bit sequence.

In FIG. 11(a), CRC generation (S1101 a), sequence generation (S1102 a),scrambling (S1103 a), channel encoding (S1105 a), and channelinterleaving (S1107 a) may be performed by a CRC code generator, asequence generator, a scrambler, a channel encoder, and a channelinterleaver, respectively. The CRC code generator, the sequencegenerator, the scrambler, the channel encoder, and the channelinterleaver may constitute a part of a processor of the transmittingdevice and may be configured to be operated under control of theprocessor of the transmitting device. In FIG. 11(b), CRC check (S1101b), sequence generation (S1102 b), descrambling (S1103 b), channeldecoding (S1105 b), and channel interleaving (S1107 b) may be performedby a CRC checker, a sequence generator, a descrambler, a channeldecoder, and a channel interleaver, respectively. The CRC checker, thesequence generator, the descrambler, the channel decoder, and thechannel interleaver may constitute a part of a processor of thereceiving device and may be configured to be operated under control theprocessor of the receiving device. In the legacy LTE system, thescrambler generates an m-sequence using a UE ID, a cell ID, and/or aslot index and then scrambles input bits consisting of information bitsand CRC bits, which are input to the scrambler, using the m-sequence.The descrambler generates an m-sequence using a UE ID, a cell ID, and/ora slot index and then descrambles input bits consisting of informationbits and CRC bits, which are input to the descrambler, using them-sequence.

Some process(es) of the encoding procedure or some process(es) of thedecoding procedure may be omitted according to types of transportchannels or types of control information. Even in an NR system as wellas the legacy LTE system, an encoding or decoding procedure similar tothe encoding or decoding procedure illustrated in FIG. 11 is used.However, the LTE system and the NR system may use different codingschemes in the channel encoding/decoding process. For example, thelegacy LTE system uses channel coding schemes listed in Table 1 andTable 2 below, whereas the NR system is expected to use an LDPC code anda Polar code for channel coding. Table 1 lists channel coding schemesand coding rates for transport blocks, used in the LTE system. Table 2lists channel coding schemes and coding rates for control information,used in the LTE system.

TABLE 1 TrCH Coding scheme Coding rate UL-SCH Turbo coding 1/3 DL-SCHPCH MCH SL-SCH SL-DCH BCH Tail biting convolutional 1/3 SL-BCH coding

TABLE 2 Control Information Coding scheme Coding rate DCI Tail bitingconvolutional 1/3 coding CFI Block code 1/16 HI Repetition code 1/3 UCIBlock code Variable Tail biting convolutional 1/3 coding SCI Tail bitingconvolutional 1/3 coding

For more details of the encoding procedure and decoding procedure of thelegacy LTE system, reference may be made to 3GPP TS 36.211, 3GPP TS36.212, 3GPP 36.331, and/or 3GPP TS 36.331. For more details of theencoding procedure and decoding procedure of the NR system, referencemay be made to 3GPP TS 38.211, 3GPP TS 38.212, 3GPP TS 38.213, 3GPP TS38.214, and/or 3GPP TS 38.331.

FIG. 12 illustrates a frame structure. The frame structure illustratedin FIG. 12 is purely exemplary and the number of subframes, the numberof slots, and/or the number of symbols in a frame may be variouslychanged. In the NR system, an OFDM numerology (e.g., subcarrier spacing(SCS)) may be differently configured between a plurality of cellsaggregated for one UE. Therefore, an (absolute time) duration of a timeresource (e.g. a subframe, a slot, or a transmission time interval(TTI)) including the same number of symbols may be differentlyconfigured between the aggregated cells. Herein, symbols may includeOFDM symbols (or CP-OFDM symbols), SC-FDMA symbols (or discrete Fouriertransform-spread-OFDM (DFT-s-OFDM) symbols).

Referring to FIG. 12, in the NR system, downlink and uplinktransmissions are organized into frames. Each frame has T_(f)=10 msduration. Each frame is divided into two half-frames, where each of thehalf-frames has 5 ms duration. Each half-frame consists of 5 subframes,where the duration T_(sf) per subframe is 1 ms. Each subframe is dividedinto slots and the number of slots in a subframe depends on a subcarrierspacing. Each slot includes 14 or 12 OFDM symbols based on a cyclicprefix (CP). In a normal CP, each slot includes 14 OFDM symbols and, inan extended CP, each slot includes 12 OFDM symbols. The following tableshows the number of OFDM symbols per slot, the number of slots perframe, and the number of slots per for the normal CP, according to thesubcarrier spacing Δf=2^(u)*15 kHz.

TABLE 3 u N^(slot) _(symb) N^(frame,u) _(slot) N^(subframe,u) _(slot) 014 10 1 1 14 20 2 2 14 40 4 3 14 80 8 4 14 160 16

The following table shows the number of OFDM symbols per slot, thenumber of slots per frame, and the number of slots per for the extendedCP, according to the subcarrier spacing Δf=2^(u)*15 kHz.

TABLE 4 u N^(slot) _(symb) N^(frame,u) _(slot) N^(subframe,u) _(slot) 212 40 4

A slot includes plural symbols (e.g., 14 or 12 symbols) in the timedomain. For each numerology (e.g. subcarrier spacing) and carrier, aresource grid of N^(size,u) _(grid,x)*N^(RB) _(sc) subcarriers andN^(subframe,u) _(symb) OFDM symbols is defined, starting at commonresource block (CRB) N^(start,u) _(grid) indicated by higher-layersignaling (e.g. radio resource control (RRC) signaling), whereN^(size,u) _(grid,x) is the number of resource blocks (RBs) in theresource grid and the subscript x is DL for downlink and UL for uplink.N^(RB) _(sc) is the number of subcarriers per RB. In the 3GPP basedwireless communication system, N^(RB) _(sc) is 12 generally. There isone resource grid for a given antenna port p, subcarrier spacingconfiguration u, and transmission direction (DL or UL). The carrierbandwidth N^(size,u) _(grid) for subcarrier spacing configuration u isgiven by the higher-layer parameter (e.g. RRC parameter). Each elementin the resource grid for the antenna port p and the subcarrier spacingconfiguration u is referred to as a resource element (RE) and onecomplex symbol may be mapped to each RE. Each RE in the resource grid isuniquely identified by an index k in the frequency domain and an index lrepresenting a symbol location relative to a reference point in the timedomain. In the NR system, an RB is defined by 12 consecutive subcarriersin the frequency domain. In the NR system, RBs are classified into CRBsand physical resource blocks, (PRBs). CRBs are numbered from 0 andupwards in the frequency domain for subcarrier spacing configuration u.The center of subcarrier 0 of CRB 0 for subcarrier spacing configurationu coincides with ‘point A’ which serves as a common reference point forresource block grids. PRBs are defined within a bandwidth part (BWP).and numbered from 0 to N^(size) _(BWP,i)−1, where i is the number of thebandwidth part. The relation between the physical resource block n_(PRB)in the bandwidth part i and the common resource block n_(CRB) is asfollows: n_(PRB)=n_(CRB)+N^(size) _(BWP,i), where N^(size) _(BWP,i) isthe common resource block where bandwidth part starts relative to CRB 0.The BWP includes a plurality of consecutive RBs in a frequency domain. Acarrier may include a maximum of N (e.g., 5) BWPs. In the 3GPP basedwireless communication system, if a UE is powered on or newly enters acell, the UE performs an initial cell search procedure of acquiring timeand frequency synchronization with the cell and detecting a physicalcell identity N^(cell) _(ID) of the cell. To this end, the UE mayestablish synchronization with the BS by receiving synchronizationsignals, e.g. a primary synchronization signal (PSS) and a secondarysynchronization signal (SSS), from the BS and obtain information such asa cell identity (ID). A UE, which has demodulated a DL signal byperforming a cell search procedure using an SSS and determined time andfrequency parameters necessary for transmitting a UL signal at anaccurate time, can communicate with a BS only after acquiring systeminformation necessary for system configuration of the UE from the BS. Inthe 3GPP based wireless communication system, the system information isconfigured by a master information block (MIB) and system informationblocks (SIBs). Each SIB includes a set of parameters associatedfunctionally with each other. The SIBs are classified into a masterinformation block (MIB), an SIB type 1 (SIB1), and other SIBs, accordingto parameters that each block includes. The MIB includes most frequentlytransmitted parameters which are essential for the UE to perform initialaccess to the network of the BS. The UE may receive the MIB over abroadcast channel (e.g., PBCH). After initial cell search, the UE mayperform a random access procedure in order to complete access to the BS.To this end, the UE may transmit a preamble over a physical randomaccess channel (PRACH) and receive a response message to the preambleover a PDCCH and a PDSCH. For reference, in a contention-based randomaccess procedure, the UE may transmit an RACH preamble (message 1(msg1)) using a PRACH resource and the BS may transmit a random accessresponse (RAR) (msg2) to the RACH preamble. The UE may transmit msg3(e.g., RRC Connection Request) using a UL grant in the RAR and the BSmay transmit a contention resolution message (msg4) to the UE. Uponcompleting the above-described procedure, the UE may perform PDCCH/PDSCHreception and PUSCH/PUCCH transmission as a normal UL/DL signaltransmission procedure.

In a legacy LTE/LTE-A system, a PSS/SSS is transmittedomni-directionally. Meanwhile, a method is considered in which a gNBwhich uses millimeter wave (mmWave) transmits a signal such as aPSS/SSS/PBCH through beamforming (BF) while sweeping beam directions.Transmission/reception of a signal while sweeping beam directions isreferred to as beam sweeping or beam scanning. In the present invention,“beam sweeping” represents a behavior of a transmitter and “beamscanning” represents a behavior of a receiver. For example, assumingthat the gNB may have a maximum of N beam directions, the gNB transmitsa signal such as a PSS/SSS/PBCH in each of the N beam directions. Thatis, the gNB transmits a synchronization signal such as the PSS/SSS/PBCHin each direction while sweeping directions that the gNB can have or thegNB desires to support. Alternatively, when the gNB can form N beams,one beam group may be configured by grouping a few beams and thePSS/SSS/PBCH may be transmitted/received with respect to each beamgroup. In this case, one beam group includes one or more beams. Thesignal such as the PSS/SSS/PBCH transmitted in the same direction may bedefined as one synchronization (SS) block and a plurality of SS blocksmay be present in one cell. When the plural SS blocks are present, SSblock indexes may be used to distinguish between the SS blocks. Forexample, if the PSS/SSS/PBCH is transmitted in 10 beam directions in onesystem, the PSS/SSS/PBCH transmitted in the same direction mayconstitute one SS block and it may be understood that 10 SS blocks arepresent in the system. In the present invention, a beam index may beinterpreted as an SS block index.

FIG. 13 illustrates the structure of a synchronization signal and PBCHblock (SSB). A slot may include a maximum of two SSBs.

Referring to FIG. 13, an SSB includes 4 consecutive OFDM symbols. A PSS,a PBCH, an SSS/PBCH, and a PBCH are transmitted on respective OFDMsymbols. The PSS may be used for UE(s) to detect a cell ID within a cellID group and the SSS may be used for UE(s) to detect the cell ID group.The PBCH is used for UE(s) to detect an SSB (time) index and ahalf-frame and includes an MIB. The PBCH includes a data resourceelement (RE) and a demodulation reference signal (DMRS) RE on each OFDMsymbol. 3 DMRS REs are present in each RB and 3 data REs are presentbetween the DMRS REs. In the 3GPP based system, an RB is defined as 12consecutive subcarriers in the frequency domain. Each RE is defined byone subcarrier in the frequency domain and one OFDM symbol in the timedomain.

The SSB is periodically transmitted at an SSB periodicity. A basic SSBperiodicity used for initial cell selection is defined as 20 ms. Aftercell access, the SSB periodicity may be set to one of {5 ms, 10 ms, 20ms, 40 ms, 80 ms, 160 ms}. An SSB burst set is configured at a startpart of each SSB periodicity. The SSB burst set includes a time windowof 5 ms and the SSB may be transmitted a maximum of L times within theSSB burst set. A candidate position of the SSB may be predefined withinthe SSB burst set. A maximum number L of transmissions of the SSB may begiven as follows according to a frequency band of a carrier.

For frequency range up to 3 GHz, L=4

For frequency range from 3 GHz to 6 GHz, L=8

For frequency range from 6 GHz to 52.6 GHz, L=64

The UE may perform DL synchronization acquisition (e.g., OFDMsymbol/slot/half-frame boundary detection), cell identifier (ID) (e.g.,physical cell identifier (PCID)) acquisition, beam arrangement forinitial access, MIB acquisition, and DL measurement, based on the SSB.

A frame number to which a detected SSB belongs may be identified bysystem frame number (SFN) information within the PBCH and a half-framenumber to which the detected SSB belongs may be identified by half-frameindication information (hereinafter, HF) within the PBCH. For example,upon detecting a PBCH including HF=0, the UE may determine that an SSBto which the PBCH belongs is contained in the first half-frame within aframe. Upon detecting a PBCH including HF=1, the UE may determine thatthe SSB to which the PBCH belongs is contained in the second half-framewithin the frame.

SSB time location is indexed (SSB index) in ascending order in time from0 to L−1 within the SSB burst set (i.e., half-frame). When L>4, 3 leastsignificant bits (LSBs) out of a 6-bit SSB index may be transmittedusing one of 8 different PBCH-DMRS sequences and 3 most significant bits(MSBs) out of the 6-bit SSB index may be transmitted through SSB indexinformation included in the PBCH. When L=4, a 2-bit SSB index may beindicated using 8 PBCH-DMRS sequences. When L=4, since the 8 PBCH-DMRSsequences may indicate a total of 3 bits, one remaining bit afterindicating the SSB index among the 3 bits capable of being indicated bythe 8 PBCH-DMRS sequences may be used to indicate a half-frame. At 6 GHzor more, 3 bits for the SSB index in the PBCH may be used to carry 3MSBs of the SSB index. At 6 GHz or less, since a 3-bit SSB index or a2-bit SSB index may be identified by 3 bits signaled by the PBCH-DMRSsequences, the 3 bits for the SSB index in the PBCH may be used asreserved bits at 3 GHz or less.

FIG. 14 illustrates a signal processing procedure of a PBCH.

For PBCH transmission in a frame, PBCH content, i.e., informationthrough the PBCH, is scrambled. The PBCH is scrambled using the firstscrambling sequence and a CRC is inserted in the scrambled PBCH. TheCRC-inserted PBCH is interleaved, encoded, and rate-matched, to obtainthe encoded PBCH. The first scrambling sequence is a gold sequenceinitialized by a physical cell ID and is determined using the second andthird LSBs of an SFN in which the PBCH is transmitted. The encoded PBCHis scrambled again using the second scrambling sequence. The secondscrambling sequence is initialized based on the physical cell ID and 3LSBs of an SSB index. The encoded PBCH scrambled using the secondscrambling sequence is transmitted on a time-frequency resource throughmodulation and RE mapping, as illustrated in FIG. 13.

In the same way as in the legacy LTE/LTE-A system, the UE that desiresto perform initial access to a specific cell in the NR system receivesthe MIB for the cell through the PBCH from the BS operating/controllingthe cell and receives SIBs and radio resource control (RRC) parametersthrough a PDSCH. Bit fields of the PBCH may include bit(s) already knownto the UE, such as SFN bits (in which an SFN is known a priori forhandover cases) and reserved bits. In the NR system, Polar codes areused for channel coding of the PBCH. If already known bit(s) are wellused during Polar encoding, channel coding performance may be improved.If an already known bit size (i.e., the number of known bits) is Kn, afrozen bit size becomes N−K+Kn. Herein, N is the size of a Polar code(i.e., a mother code size of Polar codes) and K is the size of inputinformation blocks to the Polar code, i.e., the number of informationbits input to the Polar code. For example, Polar encoding forinformation of ‘K−Kn’ bits is performed based on the following Polarsequence (see a Polar sequence defined in 3GPP TS 38.212 V1.0.0).

Polar Sequence

W I 0 0 1 1 2 2 3 4 4 8 5 16 6 32 7 3 8 5 9 64 10 9 11 6 12 17 13 10 1418 15 128 16 12 17 33 18 65 19 20 20 256 21 34 22 24 23 36 24 7 25 12926 66 27 512 28 11 29 40 30 68 31 130 32 19 33 13 34 48 35 14 36 72 37257 38 21 39 132 40 35 41 258 42 26 43 513 44 80 45 37 46 25 47 22 48136 49 260 50 264 51 38 52 514 53 96 54 67 55 41 56 144 57 28 58 69 5942 60 516 61 49 62 74 63 272 64 160 65 520 66 288 67 528 68 192 69 54470 70 71 44 72 131 73 81 74 50 75 73 76 15 77 320 78 133 79 52 80 23 81134 82 384 83 76 84 137 85 82 86 56 87 27 88 97 89 39 90 259 91 84 92138 93 145 94 261 95 29 96 43 97 98 98 515 99 88 100 140 101 30 102 146103 71 104 262 105 265 106 161 107 576 108 45 109 100 110 640 111 51 112148 113 46 114 75 115 266 116 273 117 517 118 104 119 162 120 53 121 193122 152 123 77 124 164 125 768 126 268 127 274 128 518 129 54 130 83 13157 132 521 133 112 134 135 135 78 136 289 137 194 138 85 139 276 140 522141 58 142 168 143 139 144 99 145 86 146 60 147 280 148 89 149 290 150529 151 524 152 196 153 141 154 101 155 147 156 176 157 142 158 530 159321 160 31 161 200 162 90 163 545 164 292 165 322 166 532 167 263 168149 169 102 170 105 171 304 172 296 173 163 174 92 175 47 176 267 177385 178 546 179 324 180 208 181 386 182 150 183 153 184 165 185 106 18655 187 328 188 536 189 577 190 548 191 113 192 154 193 79 194 269 195108 196 578 197 224 198 166 199 519 200 552 201 195 202 270 203 641 204523 205 275 206 580 207 291 208 59 209 169 210 560 211 114 212 277 213156 214 87 215 197 216 116 217 170 218 61 219 531 220 525 221 642 222281 223 278 224 526 225 177 226 293 227 388 228 91 229 584 230 769 231198 232 172 233 120 234 201 235 336 236 62 237 282 238 143 239 103 240178 241 294 242 93 243 644 244 202 245 592 246 323 247 392 248 297 249770 250 107 251 180 252 151 253 209 254 284 255 648 256 94 257 204 258298 259 400 260 608 261 352 262 325 263 533 264 155 265 210 266 305 267547 268 300 269 109 270 184 271 534 272 537 273 115 274 167 275 225 276326 277 306 278 772 279 157 280 656 281 329 282 110 283 117 284 212 285171 286 776 287 330 288 226 289 549 290 538 291 387 292 308 293 216 294416 295 271 296 279 297 158 298 337 299 550 300 672 301 118 302 332 303579 304 540 305 389 306 173 307 121 308 553 309 199 310 784 311 179 312228 313 338 314 312 315 704 316 390 317 174 318 554 319 581 320 393 321283 322 122 323 448 324 353 325 561 326 203 327 63 328 340 329 394 330527 331 582 332 556 333 181 334 295 335 285 336 232 337 124 338 205 339182 340 643 341 562 342 286 343 585 344 299 345 354 346 211 347 401 348185 349 396 350 344 351 586 352 645 353 593 354 535 355 240 356 206 35795 358 327 359 564 360 800 361 402 362 356 363 307 364 301 365 417 366213 367 568 368 832 369 588 370 186 371 646 372 404 373 227 374 896 375594 376 418 377 302 378 649 379 771 380 360 381 539 382 111 383 331 384214 385 309 386 188 387 449 388 217 389 408 390 609 391 596 392 551 393650 394 229 395 159 396 420 397 310 398 541 399 773 400 610 401 657 402333 403 119 404 600 405 339 406 218 407 368 408 652 409 230 410 391 411313 412 450 413 542 414 334 415 233 416 555 417 774 418 175 419 123 420658 421 612 422 341 423 777 424 220 425 314 426 424 427 395 428 673 429583 430 355 431 287 432 183 433 234 434 125 435 557 436 660 437 616 438342 439 316 440 241 441 778 442 563 443 345 444 452 445 397 446 403 447207 448 674 449 558 450 785 451 432 452 357 453 187 454 236 455 664 456624 457 587 458 780 459 705 460 126 461 242 462 565 463 398 464 346 465456 466 358 467 405 468 303 469 569 470 244 471 595 472 189 473 566 474676 475 361 476 706 477 589 478 215 479 786 480 647 481 348 482 419 483406 484 464 485 680 486 801 487 362 488 590 489 409 490 570 491 788 492597 493 572 494 219 495 311 496 708 497 598 498 601 499 651 500 421 501792 502 802 503 611 504 602 505 410 506 231 507 688 508 653 509 248 510369 511 190 512 364 513 654 514 659 515 335 516 480 517 315 518 221 519370 520 613 521 422 522 425 523 451 524 614 525 543 526 235 527 412 528343 529 372 530 775 531 317 532 222 533 426 534 453 535 237 536 559 537833 538 804 539 712 540 834 541 661 542 808 543 779 544 617 545 604 546433 547 720 548 816 549 836 550 347 551 897 552 243 553 662 554 454 555318 556 675 557 618 558 898 559 781 560 376 561 428 562 665 563 736 564567 565 840 566 625 567 238 568 359 569 457 570 399 571 787 572 591 573678 574 434 575 677 576 349 577 245 578 458 579 666 580 620 581 363 582127 583 191 584 782 585 407 586 436 587 626 588 571 589 465 590 681 591246 592 707 593 350 594 599 595 668 596 790 597 460 598 249 599 682 600573 601 411 602 803 603 789 604 709 605 365 606 440 607 628 608 689 609374 610 423 611 466 612 793 613 250 614 371 615 481 616 574 617 413 618603 619 366 620 468 621 655 622 900 623 805 624 615 625 684 626 710 627429 628 794 629 252 630 373 631 605 632 848 633 690 634 713 635 632 636482 637 806 638 427 639 904 640 414 641 223 642 663 643 692 644 835 645619 646 472 647 455 648 796 649 809 650 714 651 721 652 837 653 716 654864 655 810 656 606 657 912 658 722 659 696 660 377 661 435 662 817 663319 664 621 665 812 666 484 667 430 668 838 669 667 670 488 671 239 672378 673 459 674 622 675 627 676 437 677 380 678 818 679 461 680 496 681669 682 679 683 724 684 841 685 629 686 351 687 467 688 438 689 737 690251 691 462 692 442 693 441 694 469 695 247 696 683 697 842 698 738 699899 700 670 701 783 702 849 703 820 704 728 705 928 706 791 707 367 708901 709 630 710 685 711 844 712 633 713 711 714 253 715 691 716 824 717902 718 686 719 740 720 850 721 375 722 444 723 470 724 483 725 415 726485 727 905 728 795 729 473 730 634 731 744 732 852 733 960 734 865 735693 736 797 737 906 738 715 739 807 740 474 741 636 742 694 743 254 744717 745 575 746 913 747 798 748 811 749 379 750 697 751 431 752 607 753489 754 866 755 723 756 486 757 908 758 718 759 813 760 476 761 856 762839 763 725 764 698 765 914 766 752 767 868 768 819 769 814 770 439 771929 772 490 773 623 774 671 775 739 776 916 777 463 778 843 779 381 780497 781 930 782 821 783 726 784 961 785 872 786 492 787 631 788 729 789700 790 443 791 741 792 845 793 920 794 382 795 822 796 851 797 730 798498 799 880 800 742 801 445 802 471 803 635 804 932 805 687 806 903 807825 808 500 809 846 810 745 811 826 812 732 813 446 814 962 815 936 816475 817 853 818 867 819 637 820 907 821 487 822 695 823 746 824 828 825753 826 854 827 857 828 504 829 799 830 255 831 964 832 909 833 719 834477 835 915 836 638 837 748 838 944 839 869 840 491 841 699 842 754 843858 844 478 845 968 846 383 847 910 848 815 849 976 850 870 851 917 852727 853 493 854 873 855 701 856 931 857 756 858 860 859 499 860 731 861823 862 922 863 874 864 918 865 502 866 933 867 743 868 760 869 881 870494 871 702 872 921 873 501 874 876 875 847 876 992 877 447 878 733 879827 880 934 881 882 882 937 883 963 884 747 885 505 886 855 887 924 888734 889 829 890 965 891 938 892 884 893 506 894 749 895 945 896 966 897755 898 859 899 940 900 830 901 911 902 871 903 639 904 888 905 479 906946 907 750 908 969 909 508 910 861 911 757 912 970 913 919 914 875 915862 916 758 917 948 918 977 919 923 920 972 921 761 922 877 923 952 924495 925 703 926 935 927 978 928 883 929 762 930 503 931 925 932 878 933735 934 993 935 885 936 939 937 994 938 980 939 926 940 764 941 941 942967 943 886 944 831 945 947 946 507 947 889 948 984 949 751 950 942 951996 952 971 953 890 954 509 955 949 956 973 957 1000 958 892 959 950 960863 961 759 962 1008 963 510 964 979 965 953 966 763 967 974 968 954 969879 970 981 971 982 972 927 973 995 974 765 975 956 976 887 977 985 978997 979 986 980 943 981 891 982 998 983 766 984 511 985 988 986 1001 987951 988 1002 989 893 990 975 991 894 992 1009 993 955 994 1004 995 1010996 957 997 983 998 958 999 987 1000 1012 1001 999 1002 1016 1003 7671004 989 1005 1003 1006 990 1007 1005 1008 959 1009 1011 1010 1013 1011895 1012 1006 1013 1014 1014 1017 1015 1018 1016 991 1017 1020 1018 10071019 1015 1020 1019 1021 1021 1022 1022 1023 1023

The above table shows a Polar sequence Q₀ ^(Nmax−1) and a reliabilityW(Q_(i) ^(Nmax)) of the Polar sequence. In the above table, W denotesW(Q_(i) ^(Nmax)) and I denotes Q_(i) ^(Nmax). Namely, the Polar sequenceQ₀ ^(Nmax−1)={Q₀ ^(Nmax), Q₁ ^(Nmax), . . . , Q_(Nmax−1) ^(Nmax)} isgiven by the above table, where 0≤Q_(i) ^(Nmax)≤Nmax−1 denotes a bitindex before Polar encoding for i=0, 1, . . . , Nmax−1 and Nmax=1024.The Polar sequence Q₀ ^(Nmax−1) is ascending order of reliability W(Q₀^(Nmax))<W(Q₁ ^(Nmax))< . . . <W(Q_(Nmax−1) ^(Nmax)), where W(Q_(i)^(Nmax)) denotes the reliability of bit index Q_(i) ^(Nmax). Forexample, referring to the above table, a reliability W(Q_(i) ^(Nmax))=3of a bit index Q_(i) ^(Nmax)4 is lower than a reliability W(Q_(i)^(Nmax))=7 of bit index Q_(i) ^(Nmax)=3. That is, the above table lists,in ascending order of reliability, bit indexes 0 to 1023 whichrespectively indicate 1024 input positions of a Polar code of Nmax=1024.For any information block encoded to N bits, a same Polar sequence Q₀^(N−1)={Q₀ ^(N), Q₁ ^(N), Q₂ ^(N), . . . , Q_(N−1) ^(N)} is used. ThePolar sequence Q₀ ^(N−1) is a subset of Polar sequence Q₀ ^(Nmax−1) withall elements Q_(i) ^(Nmax) of values less than N, ordered in ascendingorder of reliability W(Q₀ ^(N))<W(Q₁ ^(N))<W(Q₂ ^(N))< . . . <W(Q_(N−1)^(N)). For example, when N=8, a Polar sequence Q₀ ⁷ includes elements ofQ_(i) ^(Nmax)<8 among elements of the Polar sequence Q₀ ^(Nmax−1) andthe elements of Q_(i) ^(Nmax)<8 are ordered in ascending order ofreliability W(0)<W(1)<W(2)<W(4)<W(3)<W(5)<W(6).

Hereinafter, the present invention will be described based on the Polarsequence Q₀ ^(Nmax−1) given by the table of <Polar sequence>.

In spite of a known bit, the known bit may be used as informationaccording to a moment when a radio signal is transmitted so that theknown bit may become an unknown bit. For example, an SFN bit is used asa known bit only during handover. Therefore, a method of fixing K andthen predetermining input positions at which known bit(s) are to bemapped to a Polar code according to the number of the known bits may beused. For example, Table 5 lists input bit positions for an informationblock of size K(=10) input to a Polar code in a Polar sequence of N=512.

TABLE 5 Polar sequence 1 505 2 506 3 479 4 508 5 495 6 503 7 507 8 509 9510 10 511

Table 5 shows 10 elements for K=10 among elements of the Polar sequenceof N=512 in ascending order of reliability. Referring to theabove-described table of <Polar sequence>, values of I having 10reliabilities W(Q_(i) ^(Nmax)) among values of I(=Q_(i) ^(Nmax)) lessthan N=512 are {479, 495, 503, 505, 506, 507, 508, 509, 510, 511}. If{479, 495, 503, 505, 506, 507, 508, 509, 510, 511} are arranged inascending order of reliability W, {505, 506, 479, 508, 495, 503, 507,509, 510, 511}, which is a set of bit indexes for K=10 in the Polarsequence of N=512 shown in Table 5, are obtained. Known bit(s) and/orunknown bit(s) among K=10 may be arranged in bit indexes {505, 506, 479,508, 495, 503, 507, 509, 510, 511} according to examples of the presentinvention.

Although the present invention is described by giving the PBCH as anexample for convenience of description, the present invention may alsobe applied to other channels using a data field in which known bit(s)such as a short PUCCH are included.

It is assumed that a set of bit indexes in a Polar sequence, for Knknown bit(s) regarded as frozen bits, is Fn. It was agreed that the PBCHhas a payload size of 56 bits in the NR system. In consideration of thisfact, method(s) (e.g. Method 1, Method 2-a, Method 2-b, Method 2-c) ofthe present invention to obtain Fn for the case in which K=56, N=512,M=864, and |Fn|=2 (i.e. Kn=2) are described. Herein, M is the length ofan actual codeword and may be equal to a size after an encoded bitsequence is rate-matched. For example, in the NR system, M for a PBCH is864. In the present disclosure, |S| represents the number of elements ina set S. Prior to a description of the methods and examples of thepresent invention, a method of obtaining 56 elements (i.e., bit indexesor input positions) for an information block of K=56 among elements of aPolar sequence of N=512 will now be described. If the method describedwith reference to Table 5 is applied, values of I having 56 highestreliabilities (i.e. 56 most reliable bit indexes) among values ofI(=Q_(i) ^(Nmax)) less than N=512 are {247, 253, 254, 255, 367, 375,379, 381, 382, 383, 415, 431, 439, 441, 443, 444, 445, 446, 447, 463,469, 470, 471, 473, 474, 475, 476, 477, 478, 479, 483, 485, 486, 487,489, 490, 491, 492, 493, 494, 495, 497, 498, 499, 500, 501, 502, 503,504, 505, 506, 507, 508, 509, 510, 511}. If the 56 bit indexes {247,253, 254, 255, 367, 375, 379, 381, 382, 383, 415, 431, 439, 441, 443,444, 445, 446, 447, 463, 469, 470, 471, 473, 474, 475, 476, 477, 478,479, 483, 485, 486, 487, 489, 490, 491, 492, 493, 494, 495, 497, 498,499, 500, 501, 502, 503, 504, 505, 506, 507, 508, 509, 510, 511} arearranged in ascending order of reliability W, a new Polar sequence {441,469, 247, 367, 253, 375, 444, 470, 483, 415, 485, 473, 474, 254, 379,431, 489, 486, 476, 439, 490, 463, 381, 497, 492, 443, 382, 498, 445,471, 500, 446, 475, 487, 504, 255, 477, 491, 478, 383, 493, 499, 502,494, 501, 447, 505, 506, 479, 508, 495, 503, 507, 509, 510, 511}consisting of the 56 bit indexes is obtained. The Polar sequence {441,469, 247, 367, 253, 375, 444, 470, 483, 415, 485, 473, 474, 254, 379,431, 489, 486, 476, 439, 490, 463, 381, 497, 492, 443, 382, 498, 445,471, 500, 446, 475, 487, 504, 255, 477, 491, 478, 383, 493, 499, 502,494, 501, 447, 505, 506, 479, 508, 495, 503, 507, 509, 510, 511} is asubset of the Polar sequence for N=512 and also is a subset for a Polarsequence for Nmax=1024.

FIG. 15 illustrates a flowchart of PBCH transmission according toexamples of the present invention. For channel coding for a Polar code,bits for a PBCH are mapped to bit positions of the Polar code (S1601).Channel coding performance differs depending on to which bit positionsof the Polar code the bits of the PBCH are mapped. In this disclosure,specific bits of the bits for the PBCH are mapped to the bit positionsof the Polar code according to example(s) of the present invention. ThePBCH, more specifically, the bits for the PBCH are encoded based on thePolar code (S1603). The encoded bits are transmitted over the PBCH(S1605).

A receiving device receives the PBCH and decodes the bits in the PBCHbased on a mapping relationship applied in S1601. The mappingrelationship may be one of the examples of the present inventiondescribed below.

Method 1. In a Polar sequence Q₀ ^(Nmax−1), if a set of bit indexes forK among bit indexes of the Polar sequence is Q*_(I, K) ^(N) and a set ofbit indexes when considering Kn (i.e., a set of bit indexes for K−Kn) isQ*_(I, Kn) ^(N), then a set of Q*_(I, K) ^(N) \ Q*_(I, Kn) ^(N) is usedas frozen bit(s), where A\B denotes the difference of set B from set A,i.e., A-B, and is the set of elements of set A that are not in set B.That is, for Fn=Q*_(I, K) ^(N) \ Q*_(I, Kn) ^(N), K=56, N=512, andKn=|Fn|=2 Fn={441, 469}. This method uses the Polar sequence Q₀^(Nmax−1) shared by a transmitting device and a receiving device and maybe useful when K or |Fn| is changed.

Method 2. Regardless of the Polar sequence Q₀ ^(Nmax−1), bit(s) making ablock error rate (BLER) lowest are used as frozen bit(s).

The following table lists bit error rate (BER) values when a target BLERis 10⁻² in the case of K=56, N=512 and M=864.

TABLE 6 i BER 247 0.00465686 253 0.00343137 254 0.00367647 2550.00367647 367 0.00220588 375 0.00563726 379 0.00416667 381 0.00661765382 0.00588235 383 0.00490196 415 0.0024509 431 0.00196078 439 0.0046568441 0.0085784 443 0.0061274 444 0.0083333 445 0.0073529 446 0.0061274447 0.0056372 463 0.0039215 469 0.0095588 470 0.0112745 471 0.0068627473 0.0102941 474 0.010049 475 0.0105392 476 0.0112745 477 0.0098039 4780.0095588 479 0.0058823 483 0.0085784 485 0.0093137 486 0.0115196 4870.007598 489 0.0115196 490 0.0107843 491 0.0078431 492 0.0120098 4930.0107843 494 0.0090686 495 0.0056372 497 0.007598 498 0.0115196 4990.0112745 500 0.0102941 501 0.0090686 502 0.0112745 503 0.0093137 5040.0093137 505 0.0120098 506 0.0125 507 0.0115196 508 0.0120098 5090.0107843 510 0.0095588 511 0.0071078

Table 6 lists the BER values according to bit indexes. FIG. 16illustrates BER values of input bit indexes for a Polar code. In FIG.16, i=1, 2, 3, . . . , 55, 56 are bit indexes {247, 253, 254, 255, 367,375, 379, 381, 382, 383, 415, 431, 439, 441, 443, 444, 445, 446, 447,463, 469, 470, 471, 473, 474, 475, 476, 477, 478, 479, 483, 485, 486,487, 489, 490, 491, 492, 493, 494, 495, 497, 498, 499, 500, 501, 502,503, 504, 505, 506, 507, 508, 509, 510, 511} for K(=56) input bits andcorrespond to one by one to the 56 bit indexes {247, 253, 254, 255, 367,375, 379, 381, 382, 383, 415, 431, 439, 441, 443, 444, 445, 446, 447,463, 469, 470, 471, 473, 474, 475, 476, 477, 478, 479, 483, 485, 486,487, 489, 490, 491, 492, 493, 494, 495, 497, 498, 499, 500, 501, 502,503, 504, 505, 506, 507, 508, 509, 510, 511}. For example, in FIG. 16,i=1 may represent a bit index 247, i=2 may represent a bit index 253,and i=3 may represent a bit index 254.

In Method 2, a few candidate groups for Fn are exemplarily describedbelow based on Table 6 or the BER graph of FIG. 16.

Method 2-a. Known bits are placed at positions having the worst BERperformance among input positions of the polar code. BLER is mainlydetermined from bits having a poor BER, i.e., bits having a high BER,among error probabilities of respective bits. Therefore, ifcorresponding parts, i.e., input bit indexes having poor BERs, are usedas the known bits, since this is like the case in which BERs in thecorresponding bits become zero, BLER is improved. In Method 2-a, forexample, |Fn|={508, 506}.

Method 2-b. Known bits are placed in bit indexes of which decoding orderis earlier based on decoding bit order. According to Method 2-b, sincethe known bits are used at an early stage of decoding, BLER is improved.When the UE decodes only an SSB index of a neighbor cell although theSSB index is not a known bit, i.e., when the UE preferentially decodesonly some bits, an unknown bit may first be mapped to a bit positionhaving fast decoding order. In other words, when it is desired to causethe receiving device to decode only an index of a neighbor cell such asan SSB index although the SSB index is not a known bit or when it isdesired to cause the receiving device to preferentially decode onlypartial bits, Fn may be determined such that an unknown bit may first bedecoded in decoding bit order. As mentioned above, in the Polar code,generally, decoding is sequentially performed starting from a low bitindex among encoder input bit indexes (i.e., bit indexes before Polarencoding). Therefore, referring to bit indexes {441, 469, 247, 367, 253,375, 444, 470, 483, 415, 485, 473, 474, 254, 379, 431, 489, 486, 476,439, 490, 463, 381, 497, 492, 443, 382, 498, 445, 471, 500, 446, 475,487, 504, 255, 477, 491, 478, 383, 493, 499, 502, 494, 501, 447, 505,506, 479, 508, 495, 503, 507, 509, 510, 511} for K=56 among bit indexesof a Polar code of N=512 and the BER of FIG. 16, |Fn| lowest bit indexesmay be selected from among bit indexes in a corresponding polarsequence. In Method 2-b, for example, |Fn|={247, 253}.

Method 2-c. Known bits are placed at positions which greatly affecterror propagation. For example, in Method 2-c, known bit(s) are placedin bit index(es) having poor BERs among bit indexes of which decodingorder is early among bit indexes of the Polar code. Generally, sincedecoding order of the front part of the Polar code, i.e., decoding orderof low bit indexes, is earlier than decoding order of the rear part ofthe Polar code, i.e., decoding order of high bit indexes, a bit positionhaving a poor BER (i.e., a bit position having a high BER) among bitpositions of the front part of the Polar code may be replaced with aknown bit. Since the Polar code uses successive decoding, if an erroroccurs in a decoding bit, an error is propagated to rear decoding bit(s)of the decoding bit in which the error occurs, thereby increasing theBER. Since, in Method 2-a, the known bit is mapped to a bit positionhaving the poorest BER among K bit positions, decoding for the known bitis performed too late if a bit index of a bit position having a poor BERis high so that it is difficult to reduce error propagation. Incontrast, according to Method 2-c, the BLER may be improved by reducingan initially generated error probability. Fn may differ according to thesize of known bits, i.e., the number of known bits. However, if knownbits are allocated to input bit indexes of a part at which decoding isperformed early, the BLER may be optimized. Optimal bit setting, i.e.,optimal Fn, may be searched by a combination of indexes within inputindexes (i.e., bit indexes) of a part at which decoding is earlyperformed relative to other parts, i.e., a part at which a decodingorder is early or by a combination of indexes which simultaneouslyconsiders the input indexes of the part at which decoding is earlyperformed relative to other parts and Method 2-a. Referring to Table 6and FIGS. 17A to 17C, in Method 2-c, for example, |Fn|={469, 375}.Referring to Table 6 or FIG. 16, although bit index 375 has a higher BERthan bit indexes 367 and 379 and bit index 469 has a higher BER than bitindexes 463 and 470, BERs of bit indexes 375 and 469 becomes 0 if knownbits are placed in bit indexes 375 and 469. Therefore, error propagationof bit indexes 375 and 469 may be reduced.

Table 7 shows performance of sets of known bits for Method 1, Method2-a, Method 2-b, and Method 2-c. In other words, Table 7 shows BLERs forFn described in Method 1, Method 2-a, Method 2-b, and Method 2-c.BLER_1, BLER_2, BLER_3, and BLER_4 represent BLERs for Method 1, Method2-a, Method 2-b, and Method 2-c, respectively. Particularly, Table 7shows respective BLERs when SNR=−9 dB, −8.5 dB, −8 dB, and −7.5.

TABLE 7 SNR[dB] BLER_1 BLER_2 BLER_3 BLER_4 −9 0.170068 0.22779 0.1972380.16488 −8.5 0.060368 0.082372 0.065638 0.05777 −8 0.01574 0.0242510.018002 0.015019 −7.5 0.003189 0.005385 0.003241 0.00305

Referring to Table 7, BLER_1 and BLER_4 entirely exhibit goodperformance in the PBCH. Accordingly, Method 1 or Method 2-c may beselected to determine input positions to the Polar code for bits of thePBCH. When K or known bits other than the PBCH vary, one of all theaforementioned methods may be selected to determine to which position ofinput positions to the Polar code corresponding information is input.

The length of known bits, i.e., the number of known bits, may differaccording to transmission timing. For example, an SFN is used as a knownbit only in the case of handover. In this way, when the number of knownbits differs according to transmission timing or transmission situation,an example of the present invention may separately use Fn into multiplesubsets. For example, in the case of the PBCH, if a subset for reservedbits is Fn_1 and a subset for SFN bits is Fn_2, then Fn is a union ofFn_1 and Fn_2 (Fn=Fn_1 U Fn_2) and |Fn|=|Fn_1|+|Fn_2|. When determiningFn, it is possible to discover a subset Fn_i having good performance inunits of a subset size. For example, if a subset for reserved bits isFn_1, since the reserved bits have a high possibility of being used asthe known bits, Fn_1 may be determined first and then Fn_2 may bedetermined. That is, when configuring Fn, it is possible to search forgood performance in units of a subset size. For example, when a subsetfor 2 reserved bits is Fn_1, then Fn_1 for the 2 reserved bits may bedetermined first and then Fn_2 including Fn_1 may be determined.

Alternatively, Fn may be configured in order of Fn_1, Fn_2, Fn_3, . . ., by regarding the unit of a subset size as one bit, e.g., by regarding|Fn_i|=1. Fn may be configured in such a way that Fn_2 including Fn_1 isdetermined and Fn_3 including Fn_2 is determined. In this method, Fn maybe sequentially selected starting from Fn_1 according to the size ofknown bits determined at a transmission timing of correspondinginformation regardless of how many times a subset is used. For example,if Fn_1 is configured to be used when an SFN is used as a known bit andFn_2 is configured to be used when the SFN is used as an unknown bit,then Fn may be selected according to the size of the known bit even ifthe SFN is frequently transmitted as the known bit. For example, Fn_4may be used to transmit information corresponding to 4 known bits andFn_1 may be used to transmit information corresponding one known bit.

In the case of the PBCH, even when distributed CRC is applied to thePBCH, it may be difficult to use early termination for an unknown bit ina decoding procedure due to a false alarm rate (FAR). Therefore, unknownbit(s) may be mapped to some of bit indexes other than Fn. However, forexample, when a receiving device can decode and use only a specific part(e.g., SSB index) without considering the FAR, known bit(s) may bemapped as in Method 2-b. Meanwhile, if a method of lowering an FAR of acorresponding part through a minimum of 1-bit CRC is used, SSB indexesmay be mapped in order of lowest BER among input indexes connected to acorresponding CRC part. For example, when the receiving deviceseparately decodes only the SSB index and performs CRC using a minimumof 1-bit CRC with respect to the decoded SSB index, the SSB index may bemapped to 3 bit indexes having the lowest BER among bit indexesconnected to a minimum of 1-bit CRC.

Hereinafter, the present invention will be described by taking bitfields of the PBCH as an example.

Table 8 lists information fields of the PBCH considered in the NRsystem. Although there are some fields in which the length of each bitfield of the PBCH used for the NR system is not specified, examples ofthe present invention will be described below using types which arefrequently mentioned in an NR standardization process for convenience ofdescription. For example, the examples of the present invention aredescribed with reference to Table 8. The length of bits of each bitfield of the PBCH, i.e., the number of bits of each bit field, may bedifferent from that shown in Table 8.

TABLE 8 Parameter Number of bits System frame number (SFN) 10 Half-frame(HF) timing 1 SSB location index 3 Configuration for CORESET for RMSI 8scheduling RAN2 3 Offset between SSB frequency domain 4 location andphysical resource block (PRB) grid in resource element (RE) levelDownlink numerology to be used for RMSI, 1 msg2/msg4 for initial accessand broadcasted other system information (OSI) Indication of the 1^(st)demodulation reference 1 signal (DMRS) position Spare 1 CRC 24 Total 56

A payload of the PBCH may include information shown in Table 8. In a56-bit payload for the PBCH, 10 bits are included in an MIB, 8 bits areincluded in a PBCH transport block, and 24 bits are CRC bits. In Table8, “SFN” denotes a system frame number in which the PBCH is transmitted,“Half-frame timing” denotes half-frame indication information(hereinafter, HF) indicating whether a half-frame to which the PBCHbelongs is the first half-frame or the second half-frame, “SSB locationindex” denotes information about 3 MSBs of an SSB index to which thePBCH belongs, and “Configuration for CORESET for RMSI scheduling”denotes configuration information about a control resource set(CORESET), which is a resource set on which a PDCCH carrying schedulinginformation about remaining system information (RMSI) except for the MIB(or RMSI except for the MIB and SIB1) is capable of being monitored bythe UE. “RAN2” denotes information included in the PBCH based on arequest of a work group related to a RAN2 layer among NR standardizationrelated working groups. For example, information through which whetherthe UE can camp on a cell in which the PBCH is transmitted can berapidly identified is “RAN2” which may be included in the PBCH. Forexample, frequency on/off related information indicating whether acorresponding frequency in which the PBCH is transmitted is in an on oroff state and cell on/off related information indicating whether acorresponding cell in which the PBCH is transmitted is in an on or offstate may be included in “RAN2”. “Offset between SSB frequency domainlocation and physical resource block (PRB) grid in resource element (RE)level” represents frequency offset related information (hereinafter, PRBoffset) for aligning an SSB and a PRB in the frequency domain when a PRBgrid for the SSB is not aligned with a PRB grid for the CRB. Forexample, the PRB offset information may be information about asubcarrier offset from subcarrier 0 in the CRB to subcarrier 0 of theSSB and may be given as an RE level (e.g., the number of subcarriers).“Downlink numerology to be used for RMSI, msg2/msg4 for initial accessand broadcasted other system information (OSI)” represents informationabout numerology (e.g., subcarrier spacing) available for, for example,an RMSI CORESET, DL transmission of an RACH procedure, and other SIinformation.

In the information of the PBCH, the SFN, the HF, and the SSB index aretiming information and are conveyed through a PBCH transport block. Forexample, the 1-bit HF, 4 LSBs of the 10-bit SFN, and 3 MSBs of the SSBindex are conveyed through the PBCH transport block. 6 MSBs of the10-bit SFN may be included in the MIB. In the case of an SSB transmittedin a frequency band of 6 GHz or more, 3 LSBs of the SSB index are nottransmitted through the payload of the PBCH and may be provided througha PBCH-DMRS sequence in each half-frame. In the case of an SSBtransmitted in a frequency band of 6 GHz or less, some or all of 3 bitsused for the SSB index in the PBCH may be used as reserved bits.

For performance improvement of Polar codes, although known bits shouldbe mapped to input positions having low reliabilities, a field typeconstituting the known bits may differ according to a PBCH transmissionsituation. For example, known bits for the PBCH may differ as follows.

Example 1: In an initial access stage, all bits of the PBCH may beunknown bits.

Example 2: As described earlier, SFN bits may be known bits (e.g., anSFN is known a priori for handover cases).

Example 3: In a target cell of the handover or a non-stand alone (NSA)cell which shall be configured together with another serving cell, sincesystem information is provided to the UE through another serving cell ora primary carrier (e.g., which is an LTE cell), information such asfrequency on/off, cell on/off, and CORESET may be known bit(s).

Example 4: Frequency band on/off information in a measurement stage maybe a known bit indicating “on”.

Example 5: Assuming that synchronization is matched, it may be assumedthat the SFN, the HF timing (i.e., HF indicator) (hereinafter, HF), andSSB index information are the same as those in a cell. For reference, iftime synchronization of a serving cell and a target cell (e.g., adifference between time when the UE receives a signal transmitted by theserving cell and time when the UE receives a signal transmitted by thetarget cell) is a value within a predetermined range (e.g., 33 μs, 3 us,or min (two SSB OFDM symbols, one data OFDM symbol)), this may representthat synchronization between the serving cell and the target cell ismatched. That is, the SFN, the HF, and the SSB index may be used asknown bits. Although it may be assumed that frame information orhalf-frame information in the PBCH is the same as that in the servingcell if synchronization of the serving cell and synchronization of acell having the PBCH (hereinafter, a target cell) match to only acertain degree according to accuracy of synchronization (at a framelevel, a half-frame level, a subframe level, a slot level, and/or anOFDM symbol level), synchronization of the serving cell andsynchronization of the target cell should be accurately matched in orderto assume that the SSB index is equal to that in the serving cell.Therefore, it may be difficult to assume in fact that the SSB index ofthe serving cell is equal in synchronization to the SSB index of thetarget cell. For example, when a synchronization condition (e.g. thecondition that UE and/or BS consider that time synchronization of twocells is consistent) is a frame granularity of 1/2, only the SFN may beknown bits and, when the synchronization condition is a framegranularity of 1/4, only the SFN and the HF may be known bits. When thesynchronization condition is two slots (i.e., 0.25 ms) having agranularity of a subcarrier spacing of 120 kHz at 6 GHz or more, the3-bit SSB index may be known bits.

Known bits may vary according to a transmission frequency as well as atransmission situation of the PBCH. For example, in a PBCH-DMRS whichmay carry 3-bit information, 2 bits among 3 bits indicated by thePBCH-DMRS may be used to indicate an SSB index at 3 GHz and the otherone bit may be used to indicate the HF at 3 GHz. Therefore, the HF maybe used as a known bit at 3 GHz or less.

The SSB index may operate as reserved bits. When the SSB index operatesas the reserved bits, the UE may not interpret the corresponding bits.For example, bits used as the SSB index information in a PBCHtransmitted in a frequency band of 6 GHz or more may operate as thereserved bits in a PBCH transmitted in a frequency band of 6 GHz orless. In this case, if the reserved bits are regarded as known bits, theSSB index may be used as the known bits. However, the SSB index may beregarded as unknown bits due to the possibility that the SSB index willbe used as bits to support a specific function in the future.

Hereinafter, examples of Polar code input positions for the PBCH will bedescribed in consideration of PBCH fields having the possibility ofbeing used as known bits among the fields of the PBCH.

Field position example 1: Known bits may be mapped to input positionshaving low reliabilities in order of the SFN, the HF, and the known SSBindex. The second and third LSBs of the SFN are used as a seed of thefirst scrambled sequence, the SFN may be first mapped to bit positionshaving low reliabilities such that the second and third LSBs of the SFNare not subject to scrambling. Alternatively, the SFN may be firstmapped in order of probabilistically best-matched synchronization, andthe HF and the known SSB indexes are mapped in order ofprobabilistically next best-matched synchronization. In other words,since an SFN of a cell in which a PBCH is transmitted has a highprobability of being matched with an SFN of a serving cell, the SFNamong the SFN, the HF, and the known SSB index is first mapped to bitpositions having low reliabilities. For example, if the SFN is 10 bits,the HF is one bit, and the known SSB index is 3 bits, the SFN is mappedto 10 input positions having the lowest reliabilities among 56 inputpositions to which a 56-bit payload of the PBCH can be mapped, the HF ismapped to an input position having the 11th lowest reliability, and theknown SSB index is mapped to input positions having the 12th to 14thlowest reliabilities.

Field position example 2: Known bits are mapped in order of the SFN andthe HF. In field position example 1, when an SSB index field is used asreserved bits, bits of the SSB index field are mapped to input positionsof a Polar code by regarding the bits of the SSB index field as unknownbits.

Field position example 3: Known bits may be mapped to input positionshaving low reliabilities in the order of the SFN, the HF, the known SSBindex, the frequency on/off bit, the cell on/off bit, and the CORESET,based on field position example 1 or in the order of the SFN, the HF,the frequency on/off bit, the cell on/off bit, and the CORESET, based onfield position example 2. Fields of the PBCH are mapped to inputpositions having low reliabilities among the input positions of thePolar code in the order of fields having the possibility of becomingknown bits from a field having the highest possibility to a field havinglowest possibility. In some cases, the possibility of becoming knownbits may vary in the order of the frequency on/off bit, the SFN, the HF,and the CORESET.

Field position example 4: Field(s) of known bits among the fields of thePBCH may be mapped to the input positions of the Polar code for the PBCHin the form in which a part (e.g., frequency on/off bit) of the RAN2bits is inserted among the second and third LSBs of the SFN, the HF, theother bits of the SFN, and the known SSB index or among the second andthird LSBs of the SFN, the HF, and the other bits of the SFN. Forexample, known bits may be mapped to input positions having lowreliabilities in the order of the second and third LSBs of the SFN, apart (e.g., frequency on/off bit) of the RAN2 bits, the HF, other bitsof the SFN, and the like.

In field position example 1, field position example 2, field positionexample 3, and field position example 4, a mapping order of PBCH fieldshaving the possibility of becoming known bits has been described. Inother words, relative input positions of the Polar code betweeninformation types in the PBCH payload have been described in fieldposition examples 1 to 4. However, the fields of the PBCH may be mappedto the input positions of the Polar code by various combinationsaccording to the probability that known bits will occur in addition tothe mapping order described in field position example 1, field positionexample 2, field position example 3, and field position example 4. Thefields of the PBCH may also be mapped by two or more combinations of themapping order described in field position example 1, field positionexample 2, field position example 3, and field position example 4.

Hereinafter, bit positions of known bits and unknown bits according toexamples of the present invention will be described in detail. In thefollowing examples, one or more fields capable of being known bits inthe payload of the PBCH may be placed in bit indexes of the Polar codein a specific order, for improvement in PBCH decoderperformance/latency.

Bit position example 1: The SSB index information may be placed at inputpositions having an early decoding order among the input positions ofthe Polar code for the PBCH. If the UE feeds back a reference signalreceived power (RSRP) by decoding an unknown SSB index, the UE may neednot decode bits other than the unknown SSB index. Accordingly, the SSBindex may be mapped to positions at which decoding is performed earliest(refer to Method 2-b). However, if an SSB index field used as reservedbits is present at a position at which decoding is performed earliest,there is a disadvantage of worsening BLER performance. Therefore, theSSB index may be placed at positions having an early decoding orderamong positions other than positions used for known bits. For example,when a total of 11 known bits is used for the SFN and the HF, referringto bit indexes {441, 469, 247, 367, 253, 375, 444, 470, 483, 415, 485,473, 474, 254, 379, 431, 489, 486, 476, 439, 490, 463, 381, 497, 492,443, 382, 498, 445, 471, 500, 446, 475, 487, 504, 255, 477, 491, 478,383, 493, 499, 502, 494, 501, 447, 505, 506, 479, 508, 495, 503, 507,509, 510, 511} for K=56 among bit indexes of the Polar code for N=512,eleven positions having the lowest reliabilities are placed in order of:{441, 469, 247, 367, 253, 375, 444, 470, 483, 415, 485}. 3 bit indexeshaving an early decoding order except for {441, 469, 247, 367, 253, 375,444, 470, 483, 415, 485}, i.e., 3 smallest bit indexes among bit indexesexcept for {441, 469, 247, 367, 253, 375, 444, 470, 483, 415, 485}, areas follows: {254, 255, 379}.

Bit position example 2: The SSB index information may be placed at inputpositions having an early decoding order among the input positions ofthe Polar code for the PBCH and the other information may be placed atpositions except for the positions at which the SSB index information isplaced. In other words, the unknown SSB index may be preferentiallymapped to input positions having an early decoding order and other knownbits may be mapped to bit positions except for the bit positions towhich the unknown SSB index is mapped. For example, the unknown SSBindex is mapped to smallest bit indexes {247, 253, 254} from {441, 469,247, 367, 253, 375, 444, 470, 483, 415, 485, 473, 474, 254, 379, 431,489, 486, 476, 439, 490, 463, 381, 497, 492, 443, 382, 498, 445, 471,500, 446, 475, 487, 504, 255, 477, 491, 478, 383, 493, 499, 502, 494,501, 447, 505, 506, 479, 508, 495, 503, 507, 509, 510, 511} which areobtained by sequentially arranging 56 bit indexes, to which the payloadof the PBCH may be mapped, in the ascending order of reliability, thesecond and third LSBs of the SFN may be mapped to two bit indexes {441,469} having lowest reliabilities, and the other bits of the SFN exceptfor the second and third LSBs of the SFN may be mapped to 8 bit indexes{367, 375, 444, 470, 483, 415, 485, 473} having the lowest reliabilitiesamong bit indexes except for the bit indexes to which the unknown SSBindex and the second and third LSBs of the SFN are mapped. One bit ofthe HF and one bit (e.g., frequency on/off related bit) of the RAN2 bitsmay be mapped in order of the next reliability. For example, one bit ofthe HF and one frequency on/off related bit may be mapped to two bitindexes having low reliabilities among bit indexes except for the bitindexes to which the unknown SSB index and the SFN are mapped. Referringto {441, 469, 247, 367, 253, 375, 444, 470, 483, 415, 485, 473, 474,254, 379, 431, 489, 486, 476, 439, 490, 463, 381, 497, 492, 443, 382,498, 445, 471, 500, 446, 475, 487, 504, 255, 477, 491, 478, 383, 493,499, 502, 494, 501, 447, 505, 506, 479, 508, 495, 503, 507, 509, 510,511} obtained by arranging the 56 bit indexes, to which the payload ofthe PBCH may be mapped, in the ascending order of reliability, the HFand one bit of the RAN2 bits may be sequentially mapped to bit indexes{474, 379} next to the last bit index ‘473’ used for the SFN.Alternatively, it is possible to sequentially map the HF and one bit ofthe RAN bits to {379, 474} according to probability of becoming a knownbit (e.g., when the probability that one of the RAN2 bits becomes aknown bit is higher than the probability that the HF becomes the knownbit). Alternatively, one bit of the HF and the frequency on/off relatedbit, i.e., one HF bit or one frequency on/off related bit, may be mappedto a position next to the unknown SSB index in decoding order. Forexample, one of the HF and the frequency on/off related bit is mapped toa bit index {255} having the earliest decoding order except for bitindexes {247, 253, 254} to which the SSB index information is mapped andthe other one bit of the HF and the frequency on/off related bit may bemapped to {474} having the lowest reliability among bit indexes exceptfor {247, 253, 254}, {255}, and {367, 375, 444, 470, 483, 415, 485, 473}for the SFN. Next, the other known bits may be mapped in order of lowreliability (i.e., from a bit index having a low reliability to a bitindex having a high reliability) and then unknown bits are mapped to bitindexes from a bit index having a low reliability to a bit index havinga high reliability. For example, the other bits of the RAN2, the cellon/off bit, and CORESET bit fields are mapped to bit indexes from a bitindex having a low reliability to a bit index having a high reliability

Bit position example 3: The SSB index information may be placed at 3 bitpositions among input positions {247, 253, 254, 255} having an earlydecoding order among the bit positions of the Polar coder for the PBCHand the HF or one bit (e.g., frequency on/off related information) ofthe RAN2 information may be placed at a bit position at which the SSBindex information is not placed among {247, 253, 254, 255}. For example,as in bit position example 2, 3 bits from the front part among {247,253, 254, 255} having an earlier decoding order may be selected for theSSB index. Alternatively, {253, 254, 255} may be selected in order of alow BER (refer to Table 6 or FIG. 16) in consideration of the case inwhich the UE decodes the SSB index and use it without CRC-CHECK. When anunknown SSB index is mapped to {253, 254, 255}, it is easy to implementmapping because the unknown SSB index is mapped to successive bitpositions. This is because, if the SSB index is mapped to successive bitpositions, successive memory addresses may be used for the SSB indexand, therefore, a reading/writing operation is facilitated to easilyimplement encoding/decoding. The position of the SFN is the same as thatin bit position example 2 and the HF bit and the frequency on/offrelated bit may be mapped to {247} and {474}, respectively.Alternatively, the position of the SFN may be the same as that in bitposition example 2 and the HF bit and the frequency on/off related bitmay be mapped to {474} and {247}, respectively. Alternatively, thesecond and third LSBs of the SFN may be placed at {441, 469} and theother bits of the SFN may be placed at {247, 367, 375, 444, 470, 483,415, 485}. One bit of the HF and one bit (e.g., frequency on/off relatedbit) of the RAN2 bits may be placed at {473, 474} or {474, 473}.

When the Polar code of N=512 is divided into a length-256 upper sub-codeand a length-256 lower sub-code, bit indexes belonging to the uppersub-code are only {247, 253, 254, 255} among 56 bit indexes {441, 469,247, 367, 253, 375, 444, 470, 483, 415, 485, 473, 474, 254, 379, 431,489, 486, 476, 439, 490, 463, 381, 497, 492, 443, 382, 498, 445, 471,500, 446, 475, 487, 504, 255, 477, 491, 478, 383, 493, 499, 502, 494,501, 447, 505, 506, 479, 508, 495, 503, 507, 509, 510, 511} and theother bit indexes belong to the lower sub-code. As mentioned previously,generally, since a decoder of the Polar code is designed to performdecoding from an upper row to a lower row of the Polar code, the uppersub-code is decoded earlier than the lower sub-code. Therefore, if theSSB index and/or the HF, or the SSB index and/or the RAN2 bit are placedat {247, 253, 254, 255}, a receiving device may decode the SSB indexand/or the HF, or the SSB index and/or the RAN2 bit mapped to {247, 253,254, 255} earlier than other information. In this case, a devicerequiring only the SSB index and/or the HF and a device requiring theSSB index and/or the RAN2 bit may terminate or complete decoding of thePBCH faster than the case in which the SSB index and/or the HF, or theSSB index and/or the RAN2 bit are mapped to other bit indexes.

In the case of bit position example 2 in which the SSB index is mappedto {247, 253, 254} and the HF or the RAN2 bit is mapped to {255}, if thedecoder desires to complete decoding of the HF (or RAN2 bit), thedecoder should perform decoding for bit indexes 248, 249, . . . , 254starting from 247. In contrast, in the case of bit position example 3 inwhich the SSB index is mapped to {253, 254, 255} and the HF or the RAN2bit is mapped to {247}, if {247} is decoded, the HF or the RAN2 bit maybe obtained.

In bit position example 1, bit position example 2, and bit positionexample 3, although the SSB index information, SSB information and HFinformation, or SSB information and RAN2 information have been describedas PBCH parameters having a fast decoding order, it is possible to placePBCH parameters other than the SSB index information, HF information,and/or RAN2 information at bit positions of the Polar code inconsideration of decoding order.

FIGS. 17A to 17C illustrate comparison of performance between bitpositions exemplified in the present disclosure. FIG. 17A is a graphillustrating BERs of 56 information bits, FIG. 17B is a graphillustrating BERs when HF is a known bit and the HF is mapped to bitindex {247}, and FIG. 17C is a graph illustrating BERs when HF is aknown bit and the HF is mapped to bit index {255}.

As mentioned previously, HF may be or may not be a known value and anSSB index may be or may not be a known value. If only the HF is a knownvalue and the SSB index is not a known value, the SSB index should bedecoded by a receiving device.

Referring to FIG. 17B, if the HF is a known value, the SSB index is nota known value, the HF is placed in bit index {247}, and the SSB index isplaced in bit indexes {253, 254, 255}, since the bit index having theearliest decoding order has been used for the known bit, there isadvantage of most effectively preventing error propagation in a decodingprocess. For example, BER performance in the example of FIG. 17B becomesbetter than BER performance illustrated in FIG. 17A by an influence ofbit index {247} having BER=0 due to an SC decoding characteristic inwhich decoding of indexes is performed in (nearly) ascending order. Fora similar reason, improved BERs of 4 bits placed in bit indexes {247,253, 254, 255} have an effect on BER performance of bits placed in otherbit indexes so that entire BER performance of the 56 information bitscan be improved.

Referring to FIG. 17C, if the HF is a known value, the SSB index is nota known value, the HF is placed in bit index {255}, and the SSB index isplaced in bit indexes {247, 253, 254}, a BER of bit index {255} in whichthe HF known to the UE is placed is 0 but BERs of {247, 253, 254} arealmost similar to BERs of FIG. 17A. In the example of FIG. 17C, althoughBER performance is slightly improved by sequential decoding, the HFaffects only bit index {255} so that a degree of improvement in BERperformance is lowered as compared with FIG. 17B.

Meanwhile, if the SSB index is a known value and the HF is an unknownvalue, the HF should be decoded by the receiving device. If the HF isplaced in bit index {247}, the receiving device may identify the valueof this HF more quickly as compared with the case in which the HF isplaced in bit index {255}.

FIG. 18 illustrates timing information bit fields included in an SSB.

Some bits among 3 bits used for an SSB index in a PBCH may be used for aspecific usage. For example, since 3 bits of an unknown SSB index fieldmay operate as reserved bits at 6 GHz or less, a part of the 3 bits usedfor the SSB index information at 6 GHz or more may be used as otherinformation at 6 GHz or less. For example, one of the 3 bits used forthe SSB index at 6 GHz or more may be used for PRB offset information at6 GHz or less. If one of the 3 bits used for the SSB index at 6 GHz ormore is used for the PRB offset information at 6 GHz or less, the PRBoff information may indicate a total of 32 values by 4 bits for the PRBoffset information of Table 8 and one reserved bit at below 6 GHz. Forexample, if an unknown SSB index is placed at {253, 254, 255} among thebit positions of the Polar code, b3, b4, and b5, which are 3 MSBs of theSSB index in FIG. 18, may be mapped to {253, 254, 255} in order of b3,b4, and b5 at 6 GHz or more. A part of b3, b4, and b5 at 6 GHz or lessmay be used for a specific usage. For example, a part of b3, b4, and b5at 6 GHz or less may be selected for information of specific usage(hereinafter, specific information).

Selection of one bit:

Reserved bit use example 1-1: A bit mapped to {253} having the earliestdecoding order, i.e., b3, may be selected.

Reserved bit use example 1-2: Specific information may be placed at{254} or {255}. In this case, specific information of a length-256 uppersub-code and a length-256 lower sub-code in a length-512 Polar code isplaced at one of the last two bits of the upper sub-code. When areserved bit may be regarded as a known bit, if {254} is regarded as theknown bit, a bit of {254} may not be re-encoded. Therefore, if the bitb4 (i.e., {254}) or the bit b5 (i.e., {255}) is used for the specificusage, least complexity may be obtained.

Selection of two bits:

Reserved bit use example 2-1: The bits b3 and b4 mapped to {253, 254}having an early decoding order may be selected.

Reserved bit use example 2-2: Referring to FIG. 8 for example, adecoding operation method for odd terms u1, u3, u5, and u7 among u1 tou8 is different from a decoding operation method for even terms u2, u4,u6, and u8 among u1 to u8. In consideration of this point, the bits b3and b5 placed at lower positions among the last 4 bit positions of anupper sub-code for which a decoder can perform the same operation may beselected.

Reserved bit use example 2-3: The bits b4 and b5 having the leastdecoding complexity may be selected among {253, 254, 255}.

Selection of 3 bits: All of the bits b3, b4, and b5 are used for thespecific information when 3 bits are used for the specific information.

In order for a part among the bits b3, b4, and b5 to perform a specificrole, the positions of b3, b4, and b5 may be changed within bit indexes{253, 254, 255} for an unknown SSB index.

Case in which b3 performs a specific role:

Reserved bit use example 3-1: b3 may be placed at {253}. Since {253} isthe position of b3, b3 is mapped to {253} without change in position.

Reserved bit use example 3-2: For the same reason as reserved bit useexample 1-2, b3 may be placed at {254} or {255}.

Similarly, if b4 or b5 performs a specific role, b4 or b5 may be placedat {253}, {254}, or {255} as in reserved bit use example 3-1 andreserved bit use example 3-2.

As in reserved bit use example 3-1, when the position of a bitperforming a specific role is the same as an original position, theother bits may maintain the same positions. However, as in reserved bituse example 3-2, if the position of the bit performing a specific roleis different from the original position, positions of the other bit(s)may be determined as follows.

Reserved bit use example 4-1: Among the bits b3, b4, and b5 of the SSBindex, a bit which has been placed at a bit index at which a bitperforming a specific role is to be placed is placed at a bit index atwhich the bit performing the specific role has been placed. For example,when b3 is a bit performing a specific role and b3 is desired to beplaced at {254}, b4 which has been placed at {254} is placed at {253}which is an original position of b3. Therefore, bit indexes of b4, b3,and b5 are {253, 254, 255}.

Reserved bit use example 4-2: The bits b3, b4, and b5 of the SSB indexmay be shifted using a cyclic shifter from an original position of a bitperforming a specific role to a position to be changed. For example,when b3 is a bit performing a specific role and b3 is desired to beplaced at {254}, bit positions of the Polar code for b5, b3, and b4 areplaced at{253, 254, 255} if a right shifter is used.

When two bits simultaneously perform a specific role, for example, whenb3 and b4 perform a specific role, bit indexes may be selected asfollows.

Reserved bit use example 5-1: b3 and b4 may be placed at {253, 254}which are original positions. Alternatively, b3 and b4 may be placed at{253, 254} having a fast decoding order.

Reserved bit use example 5-2: b3 and b4 may be placed at {253, 255}placed at lower positions among the last 4 bit positions of an uppersub-code, where the last 4 bit positions are bit positions for which thedecoder can perform the same operation or calculation.

Reserved bit use example 5-3: Since {254, 255} are the last two bitpositions of a length-256 upper sub-code of the length-512 Polar codeand thus have least complexity, b3 and b4 may be placed at {254, 255}.

In reserved bit use examples 5-1, 5-2, and 5-3, positions at which twobits are placed may be interchanged. For example, b3 and b4 may bemapped to {253, 254} or {254, 255}. For a similar reason, when b3 and b5or b4 and b5 perform a specific role, those bits may be placed at bitpositions of the Polar code as in the reserved bit use examples 5-1,5-2, and 5-3.

When positions of two bits performing a specific role are same asoriginal positions, positions of the other bits are identicallymaintained. However, if two bits performing a specific role aredifferent from original positions, positions of the other bits (e.g.,bit indexes) may be determined as follows.

Reserved bit use example 6-1: Among the bits b3, b4, and b5 of the SSBindex, bits which have been placed at bit indexes at which bitsperforming a specific role are to be placed are placed at bit indexes atwhich the bits performing a specific role have been placed. For example,if b3 and b5 perform a specific role and are desired to be placed at{253, 254}, the bit placed at {253} is mapped to {253} which is the samebit position as an original bit position and b5 which has been placed at{255} is placed at {254} which is an original bit position of b4. Then,the positions of b3, b5, and b4 are {253, 254, 255}.

If a cyclic shifter is used without using bit position exchange (referto the reserved bit use example 6-1) of each bit, b3, b4, and b5 may beplaced at bit positions of the Polar code as in the reserved bit useexamples 5-1, 5-2, and 5-3. For example, when a right cyclic shifter isused, b3, b4, and b5, b5, b3, and b4, or b4, b5, and b3 may be placed at{253, 254, 255}.

When two or more bits simultaneously perform a specific role, a methodof directly exchanging bit positions as in reserved bit use example 4-1and the reserved bit use example 6-1 and a method of using the cyclicshifter as in the reserved bit use examples 5-1, 5-2, and 5-3 may besimultaneously applied so that b3, b4, and b5 may be mapped to desiredbit positions. Since the bit positions are positions for the input bitsof the Polar code, in the case of uplink control information (UCI), thebits illustrated in FIG. 18 may be placed at the bit positions of thePolar code in consideration of an interleaver effect caused bydistributed CRC. For example, if bits input to the second, third, andfifth input bit positions among input bit positions of a distributed-CRCinterleaver are configured to be mapped to bit indexes {253, 254, 255}of the Polar code, then b3, b4, and b5 are placed at the second, third,and fifth input bit positions of a front part of the distributed-CRCinterleaver.

FIG. 19 is a block diagram illustrating elements of a transmittingdevice 10 and a receiving device 20 for implementing the presentinvention.

The transmitting device 10 and the receiving device 20 respectivelyinclude transceivers 13 and 23 capable of transmitting and receivingradio signals carrying information, data, signals, and/or messages,memories 12 and 22 for storing information related to communication in awireless communication system, and processors 11 and 21 operationallyconnected to elements such as the transceivers 13 and 23 and thememories 12 and 22 to control the elements and configured to control thememories 12 and 22 and/or the transceivers 13 and 23 so that acorresponding device may perform at least one of the above-describedexamples of the present invention. The transceivers may also be referredto as radio frequency (RF) units.

The memories 12 and 22 may store programs for processing and controllingthe processors 11 and 21 and may temporarily store input/outputinformation. The memories 12 and 22 may be used as buffers.

The processors 11 and 21 generally control the overall operation ofvarious modules in the transmitting device and the receiving device.Especially, the processors 11 and 21 may perform various controlfunctions to implement the present invention. The processors 11 and 21may be referred to as controllers, microcontrollers, microprocessors, ormicrocomputers. The processors 11 and 21 may be implemented by hardware,firmware, software, or a combination thereof. In a hardwareconfiguration, application specific integrated circuits (ASICs), digitalsignal processors (DSPs), digital signal processing devices (DSPDs),programmable logic devices (PLDs), or field programmable gate arrays(FPGAs) may be included in the processors 11 and 21. Meanwhile, if thepresent invention is implemented using firmware or software, thefirmware or software may be configured to include modules, procedures,functions, etc. performing the functions or operations of the presentinvention. Firmware or software configured to perform the presentinvention may be included in the processors 11 and 21 or stored in thememories 12 and 22 so as to be driven by the processors 11 and 21.

The processor 11 of the transmitting device 10 performs predeterminedcoding and modulation for a signal and/or data scheduled to betransmitted to the outside by the processor 11 or a scheduler connectedwith the processor 11, and then transfers the coded and modulated datato the transceiver 13. For example, the processor 11 converts a datastream to be transmitted into K layers through demultiplexing, channelcoding, scrambling, and modulation. The coded data stream is alsoreferred to as a codeword and is equivalent to a transport block whichis a data block provided by a MAC layer. One transport block (TB) iscoded into one codeword and each codeword is transmitted to thereceiving device in the form of one or more layers. For frequencyup-conversion, the transceiver 13 may include an oscillator. Thetransceiver 13 may include N_(t) (where N_(t) is a positive integer)transmit antennas.

A signal processing process of the receiving device 20 is the reverse ofthe signal processing process of the transmitting device 10. Undercontrol of the processor 21, the transceiver 23 of the receiving device20 receives radio signals transmitted by the transmitting device 10. Thetransceiver 23 may include N_(r) (where N_(r) is a positive integer)receive antennas and frequency down-converts each signal receivedthrough receive antennas into a baseband signal. The processor 21decodes and demodulates the radio signals received through the receiveantennas and restores data that the transmitting device 10 intended totransmit.

The transceivers 13 and 23 include one or more antennas. An antennaperforms a function for transmitting signals processed by thetransceivers 13 and 23 to the exterior or receiving radio signals fromthe exterior to transfer the radio signals to the transceivers 13 and23. The antenna may also be called an antenna port. Each antenna maycorrespond to one physical antenna or may be configured by a combinationof more than one physical antenna element. The signal transmitted fromeach antenna cannot be further deconstructed by the receiving device 20.An RS transmitted through a corresponding antenna defines an antennafrom the view point of the receiving device 20 and enables the receivingdevice 20 to derive channel estimation for the antenna, irrespective ofwhether the channel represents a single radio channel from one physicalantenna or a composite channel from a plurality of physical antennaelements including the antenna. That is, an antenna is defined such thata channel carrying a symbol of the antenna can be obtained from achannel carrying another symbol of the same antenna. A transceiversupporting a MIMO function of transmitting and receiving data using aplurality of antennas may be connected to two or more antennas.

The transmitting device 10 or the processor 11 thereof may be configuredto include a Polar encoder according to the present invention. Thereceiving device 20 and the processor 21 thereof may be configured to aPolar decoder according to the present invention.

In a few scenarios, functions, procedures, and/or methods disclosed inthis specification may be implemented by a processing chip. Theprocessing chip may be called a system-on-chip (SoC) or a chipset. Theprocessing chip may include a processor and a memory and may be mountedor installed in each of the communication devices 10 and 20. Theprocessing chip may be configured to perform or control any one of themethods and examples disclosed in the present specification or suchmethods or examples may be performed by a communication device in or towhich the processing chip is mounted/installed or connected. Thetransmitting device 10 and/or the receiving device 20 illustrated inFIG. 19 may be the communication device. The memory included in theprocessing chip may be configured to store software code or programsincluding indications causing the processor or the communication deviceto perform some or all of the functions, methods, and examples disclosedin the present specification when being executed by the processor or thecommunication device. The memory included in the processing chip may beconfigured to store or buffer information or data generated by theprocessor of the processing chip or information recovered or obtained bythe processor of the processing chip. One or more processes involvingtransmission or reception of the information or the data may beperformed by the processor or under control of the processor. Forexample, the processor may transmit a signal including information ordata to a transceiver operably connected to or coupled to the processingchip or control the transceiver to transmit a radio signal including theinformation or data. The processor may be configured to receive a signalincluding information or data from the transceiver operably connected toor coupled to the processing chip and obtain the information or datafrom the signal.

For example, the processor 11 connected to or mounted in thetransmitting device 10 may be configured to map specific bits of a PBCHto bit positions of a Polar code according to any one of the examples ofthe present invention. The processor 11 may encode the PBCH or controlthe Polar encoder to encode the PBCH, based on the Polar code. Theprocessor 11 may be configured to transmit a signal (e.g., a basebandsignal) including the PBCH to the transceiver 13 connected to theprocessor 11. The processor 11 may control the transceiver 13 totransmit a radio signal including the PBCH. The processor 21 connectedto or mounted in the receiving device 20 may be configured to decodebits of the PBCH according to any one of the examples of the presentinvention. For example, the processor 21 may decode the PBCH using thePolar code or control the Polar decoder to decode the PBCH, based on amapping relationship between specific bits of the PBCH and bit indexesof the Polar code. The processor 21 may control the transceiver 23connected to the processor 21 to receive a radio signal including thePBCH. The processor 21 may control the transceiver 23 to down-convertthe radio signal into a baseband signal. The processor 21 may receive abaseband signal including the PBCH from the transceiver 23.

The processor 11 connected to or mounted in the transmitting device maybe configured to map information, which is to be transmitted through thePBCH based on a Polar sequence shared between the transmitting deviceand the receiving device, to bit positions of a Polar code of sizeN=512. The information may include half-frame information and asynchronization signal and PBCH block (SSB) index information. Thehalf-frame information may be 1 bit and the SSB index information may be3 bits. The processor 11 may be configured to map the half-frameinformation to bit position 247 among bit positions 0 to 511 of thePolar code and map the SSB index information to bit positions 253, 254,and 255 of the Polar code. The processor 11 may be configured to encodethe information based on the Polar code. The processor 11 may include aPolar encoder configured to encode the information based on the Polarcode. The processor 11 may transmit the PBCH including the encodedinformation to the transceiver 13. The transceiver 13 may transmit aradio signal including the PBCH on a cell under control of the processor11. The processor 11 may configure a payload of the PBCH by a total of56 bits. The information within the PBCH may include a system framenumber of a frame in which the PBCH is transmitted. The processor 11 maybe configured to map the second bit and third least significant bits(LSBs) of the system frame number to bit positions 441 and 469 of thePolar code, respectively. The processor 11 may be configured to theother 8 bits of the system frame number to bit positions 367, 375, 415,444, 470, 473, 483 and 485 of the Polar code, respectively.

The transceiver 23 of the receiving device receives the radio signalincluding the PBCH on the cell. The processor 23 connected to or mountedin the receiving device may be configured to decode, based on the Polarcode of size N=512, the information within the PBCH based on the Polarsequence shared between the transmitting device and the receivingdevice. The processor 23 may include a Polar decoder configured todecode the information within the PBCH based on the Polar code of sizeN=512. The processor 23 or the Polar decoder may be configured to decodethe information based on a mapping relationship between the informationand bit positions of the Polar code. The information may includehalf-frame information and synchronization signal and PBCH block (SSB)index information. The half-frame information may be 1 bit and the SSBindex information may be 3 bits. The mapping relationship may include:mapping the half-frame information to bit position 247 among bitpositions 0 to 511 of the Polar code and mapping the SSB indexinformation to bit positions 253, 254, and 255 of the Polar code. Theprocessor 23 may be configured to obtain the PBCH payload of a total of56 bits from a signal of the PBCH. The information within the PBCH mayinclude a system frame number of a frame in which the PBCH istransmitted. The mapping relationship may further include: mapping thesecond and third least significant bits (LSBs) of the system framenumber to bit positions 441 and 469 of the Polar code, respectively. Themapping relationship may further include: mapping the other 8 bits ofthe system frame number to bit positions 367, 375, 415, 444, 470, 473,483 and 485 of the Polar code, respectively. The processor 23 may obtainthe system frame number by decoding a signal received on a PBCH resourcebased on the mapping relationship.

The Polar sequence may be a sequence arranging bit indexes 0 to 511corresponding one by one to bit positions 0 to 511 of the Polar code inascending order of reliability.

As described above, the detailed description of the preferredimplementation examples of the present invention has been given toenable those skilled in the art to implement and practice the invention.Although the invention has been described with reference to exemplaryexamples, those skilled in the art will appreciate that variousmodifications and variations can be made in the present inventionwithout departing from the spirit or scope of the invention described inthe appended claims. Accordingly, the invention should not be limited tothe specific examples described herein, but should be accorded thebroadest scope consistent with the principles and novel featuresdisclosed herein.

Examples of the present invention may be used for a processing chipconnected to or mounted in a BS, a UE, or a communication device in awireless communication system, or for other equipment.

What is claimed is:
 1. A base station configured to transmit a physicalbroadcast channel (PBCH) in a wireless communication system, the basestation comprising: a transceiver; at least one processor; and at leastone computer memory operably connectable to the at least one processorand storing instructions that, when executed, cause the at least oneprocessor to perform operations comprising: mapping information bits forthe PBCH to input bit positions of a Polar code of size N=512, based ona Polar sequence; encoding the information bits based on the Polar code;and transmitting the PBCH based on the encoded information bits, whereinthe information bits for the PBCH include (i) 1 bit related tohalf-frame information and (ii) 3 bits related to a synchronizationsignal and PBCH block (SSB) index, wherein mapping the information bitsfor the PBCH to input bit positions of the Polar code further comprises:mapping the 1 bit related to the half-frame information to input bitposition 247 among input bit positions 0 to 511 of the Polar code basedon the Polar sequence, and mapping the 3 bits related to the SSB indexto input bit positions 253, 254, and 255 among the input bit positions 0to 511 of the Polar code based on the Polar sequence.
 2. The basestation according to claim 1, wherein the number of the information bitsis
 56. 3. The base station according to claim 1, wherein the Polarsequence includes a sequence with bit indexes 0 to 511 that arranges theinput bit positions 0 to 511 of the Polar code in ascending order ofreliability.
 4. The base station according to claim 1, wherein theinformation bits for the PBCH further include 10 bits related to asystem frame number (SFN) for a frame to which the PBCH belongs, andwherein mapping the information bits for the PBCH to input bit positionsof the Polar code further comprises: mapping the second and third leastsignificant bits of the 10 bits related to the SFN to input bitpositions 441 and 469 of the Polar code, respectively, and mapping theother 8 bits of the 10 bits related to the SFN to input bit positions367, 375, 415, 444, 470, 473, 483 and 485 of the Polar code.
 5. The basestation according to claim 1, wherein transmitting the PBCH comprises:transmitting the PBCH with a demodulation reference signal for the PBCH.6. A user equipment configured to receive a physical broadcast channel(PBCH) in a wireless communication system, the user equipmentcomprising: a transceiver; at least one processor; and at least onecomputer memory operably connectable to the at least one processor andstoring instructions that, when executed, cause the at least oneprocessor to perform operations comprising: receiving the PBCH; anddecoding the PBCH the PBCH based on a Polar code of size N=512 to obtaininformation bits, wherein decoding the PBCH comprises decoding the PBCHbased on a mapping relationship between the information bits and inputbit positions of the Polar code, wherein the information bits include(i) 1 bit related to half-frame information and (ii) 3 bits related to asynchronization signal and PBCH block (SSB) index, and wherein themapping relationship comprises: mapping the 1 bit related to thehalf-frame information to input bit position 247 among input bitpositions 0 to 511 of the Polar code, and mapping the 3 bit related tothe SSB index to input bit positions 253, 254, and 255 among the inputbit positions 0 to 511 of the Polar code.
 7. The user equipmentaccording to claim 6, wherein the number of the information bits is 56.8. The user equipment according to claim 6, wherein the mappingrelationship between the information bits and the input bit positions ofthe Polar code is based on a Polar sequence, wherein the Polar sequenceincludes a sequence with bit indexes 0 to 511 that arranges the inputbit positions 0 to 511 of the Polar code in ascending order ofreliability.
 9. The user equipment according to claim 6, wherein theinformation bits further include 10 bits related to a system framenumber (SFN) for a frame to which the PBCH belongs, and wherein themapping relationship further comprises: mapping the second and thirdleast significant bits of the 10 bits related to the SFN to input bitpositions 441 and 469 of the Polar code, respectively, and mapping theother 8 bits of the 10 bits related to the SFN to bit positions 367,375, 415, 444, 470, 473, 483 and 485 of the Polar code.
 10. The userequipment according to claim 6, wherein receiving the PBCH comprises:receiving the PBCH with a demodulation reference signal for the PBCH.11. An apparatus, the apparatus comprising, at least one processor; andat least one computer memory operably connectable to the at least oneprocessor and storing instructions that, when executed, cause the atleast one processor to perform operations comprising: receiving aphysical broadcast channel (PBCH); and decoding the PBCH based on aPolar code of size N=512 to obtain information bits, wherein decodingthe PBCH comprises decoding the PBCH based on a mapping relationshipbetween the information bits and input bit positions of the Polar code,wherein the information bits include (i) 1 bit related to half-frameinformation and (ii) 3 bits related to a synchronization signal and PBCHblock (SSB) index, and wherein the mapping relationship comprises:mapping the 1 bit related to the half-frame information to input bitposition 247 among input bit positions 0 to 511 of the Polar code, andmapping the 3 bit related to the SSB index to input bit positions 253,254, and 255 among the input bit positions 0 to 511 of the Polar code.12. The apparatus according to claim 11, wherein the number of theinformation bits is
 56. 13. The apparatus according to claim 11, whereinthe mapping relationship between the information bits and the input bitpositions of the Polar code is based on a Polar sequence, wherein thePolar sequence includes a sequence with bit indexes 0 to 511 thatarranges the input bit positions 0 to 511 of the Polar code in ascendingorder of reliability.
 14. The apparatus according to claim 11, whereinthe information bits further include 10 bits related to a system framenumber (SFN) for a frame to which the PBCH belongs, and wherein themapping relationship further comprises: mapping the second and thirdleast significant bits of the 10 bits related to the SFN to input bitpositions 441 and 469 of the Polar code, respectively, and mapping theother 8 bits of the 10 bits related to the SFN to bit positions 367,375, 415, 444, 470, 473, 483 and 485 of the Polar code.
 15. Theapparatus according to claim 11, wherein receiving the PBCH comprises:receiving the PBCH with a demodulation reference signal for the PBCH.16. A computer readable non-transitory storage medium storinginstructions that, when executed by at least one processor, cause the atleast one processor to perform operations comprising: receiving aphysical broadcast channel (PBCH); and decoding the PBCH based on aPolar code of size N=512 to obtain information bits, wherein decodingthe PBCH comprises decoding the PBCH based on a mapping relationshipbetween the information bits and input bit positions of the Polar code,wherein the information bits include (i) 1 bit related to half-frameinformation and (ii) 3 bits related to a synchronization signal and PBCHblock (SSB) index, and wherein the mapping relationship comprises:mapping the 1 bit related to the half-frame information to input bitposition 247 among input bit positions 0 to 511 of the Polar code, andmapping the 3 bit related to the SSB index to input bit positions 253,254, and 255 among the input bit positions 0 to 511 of the Polar code.17. The computer readable non-transitory storage medium according toclaim 16, wherein the number of the information bits is
 56. 18. Thecomputer readable non-transitory storage medium according to claim 16,wherein the mapping relationship between the information bits and theinput bit positions of the Polar code is based on a Polar sequence,wherein the Polar sequence includes a sequence with bit indexes 0 to 511that arranges the input bit positions 0 to 511 of the Polar code inascending order of reliability.
 19. The computer readable non-transitorystorage medium according to claim 16, wherein the information bitsfurther include 10 bits related to a system frame number (SFN) for aframe to which the PBCH belongs, and wherein the mapping relationshipfurther comprises: mapping the second and third least significant bitsof the 10 bits related to the SFN to input bit positions 441 and 469 ofthe Polar code, respectively, and mapping the other 8 bits of the 10bits related to the SFN to bit positions 367, 375, 415, 444, 470, 473,483 and 485 of the Polar code.
 20. The computer readable non-transitorystorage medium according to claim 16, wherein receiving the PBCHcomprises: receiving the PBCH with a demodulation reference signal forthe PBCH.